There are books and articles about the Soviet submarine K-129 and the USS Scorpion in 1968, with various stories of attempted nuclear attacks and reprisals. Is there a factual narrative about these events (or non-events, if that's the case)?
The original source for the stories you heard is apparently the book "Scorpion Down" by Ed Offley. The book's statements are questionable to say the least and this book review makes a good point.
I checked what the Russian sources say about K-129. This 2008 interview with Viktor A. Dygalo, the commander of the division that K-129 belonged to, covers this topic among others and should be as close to the truth as one can get (at least on the Russian side):
Obviously, the American side denies involvement of the USS Swordfish in the accident - supposedly it was damaged in an ice pack and wasn't even close to the area in question. But a retaliation by Soviets would have been a reasonable assumption - if there were any convincing evidence to support this theory. As it stands now, there are many speculations about these two incidents but not much linking them together.
According to a 1999 article by Mark A. Bradley in Proceedings, the U.S. Naval Institute's professional journal ("Why They Called the Scorpion "Scrapiron," July 1998), on May 20, 1968, the Scorpion was ordered to intercept a Soviet flotilla near the Azores that included one Echo-II-class nuclear-propelled submarine, a submarine rescue vessel, two hydrographic survey ships, and eventually, a guided-missile destroyer, capable of firing nuclear surface-to-surface missiles, and an oiler. There was concern that the Soviet vessels might try to investigate or interfere with NATO underwater listening devices known as SOSUS which had been set up in that area. The court of inquiry that investigated the Scorpion's loss first considered the possibility of an underwater dog-fight between Scorpion and the Echo II sub. The court, armed with SOSUS data that would have detected such a fight, found that there was no evidence to support the theory of a battle loss. Moreover, by the time of her last report, there was no other Soviet or Warsaw-Pact, plus the panel concluded that the Echo, which was designed for launching missiles while surfaced, would not have been a match for the Scorpion.
The court also considered the possibility that one of the boat's own torpedos had exploded. In December 1967, the Scorpion had a problem when a Mark 37 torpedo accidently activated while in its tube. The danger was avoided when the boat expelled the torpedo before it could detonate. But the court initially found no direct evidence that the boat was sunk by one of its own torpedos.
After pieces of the Scorpion were recovered by the deep submersible Trieste II, a Technical Advisory Group of scientists and former submariners poured through physical evidence and SOSUS data and came up with a surprising fact -- the Scorpion had been heading east, instead of west toward Norfolk, when the first cataclysmic explosion detonated. The advisors, headed by Dr. John Craven, estimated that the first sound to register on SOSUS had been caused by at least 30 pounds of TNT, exploding 60 feet or more below the surface, and theorized that the Scorpion had been engaged in a hastily ordered U-turn in a desperate attempt to disarm a hot-run torpedo that exploded and caused uncontrollable flooding. In an article published in The Virginian-Pilot & Ledger-Star, Craven indicated that the hot-run scenario was the only one that fit all the evidence.
Craven indicated, also, that photographs taken by Trieste II showed that the torpedo room-area on the Scorpion had not imploded, as had the rest of the boat, in the deep water.
Viewing this evidence, the court of inquiry concluded that the captain had armed his torpedos while observing the Soviet flotilla, and had ordered the weapons to be disarmed before the boat returned to Norfolk, following strict rules forbidding docking in Norfolk with armed torpedos. Bradley wrote: "the investigators theorized that something as simple as a short in a piece of testing equipment accidentally could have activated one of the Mark 37's batteries and triggered a hot run. Left with only seconds to react, Commander Slattery would have ordered the Scorpion into the abrupt U-turn she was making when the torpedo exploded."
The court of inquiry's theory was hotly contested by the Navy's weapons bureau which argued that had a torpedo blown inside the torpedo room, it would have set off a chain reaction of explosions from the other torpedos, yet, there was no evidence of multiple explosions either in the photographs or the sound evidence.
Other theories were considered, including a faulty trash ejection system in the galley, resulting in massive flooding, or a battery explosion.
Bradley, finally addresses that the Scorpion was supposed to receive a full SUBSAFE overhaul to make material and structural corrections deemed necessary following the loss of the USS Thresher. Pressing military requirements, however, prevented her from receiving a full overhaul -- one that should have taken 2 years and cost $20 million. Instead, when she left on her last patrol, she had 109 pending work orders:
Bradley relates a series of stories published in The Houston Chronicle about the poor material condition of the Scorpion when she deployed. It quoted Machinist's Mate Second Class David Burton Stone who wrote home saying that the crew had repaired, replaced, or jury-rigged every piece of the Scorpion's equipment. It noted, also that on March 23, 1968, Commander Slattery drafted an emergency request for repairs that warned, among other things, that the "the hull was in a very poor state of preservation"—the Scorpion had been forced to undergo an emergency dry-docking in New London, Connecticut, immediately after her reduced overhaul because of this—and bluntly stated that "Delay of the work an additional year could seriously jeopardize the Scorpion's material readiness." Among the captain's concers was a series of leaking valves that caused the Scorpion to be restricted to an operating depth of just 300 feet, 200 feet more shallow than SUBSAFE restrictions and 400 shallower than her pre-Thresher standards.
The Navy has never pinned blame for the Scorpion's loss, although it has fully rebutted the argument that there was a battle loss. Bradley concludes that the most likely cause was what Admiral Hyman Rickover had blamed: inadequate design, poor fabrication methods, and inadequate inspections. Bradley also blames the loss on the urgency with which the Navy sought to build and deploy its nuclear submarines to compete with a growing Soviet naval threat.
Each of these submarines were sunk in separate incidents, so I wanted to make sure that anyone seeing this understood that these two were not directly involved with one another in any form of conflict. The Soviet sub K-129 was sunk a few weeks prior to the loss of the USS Scorpion, and some theories suggest that the Scorpion was sunk in retaliation for the loss of the K-129.
I found a rather extensive discussion on the USS Scorpion which provides another theory. It appears that the Scorpion was sent out of her way to spy on Soviet naval operations off the coast of Africa. There are some who believe that the Soviets discovered the Scorpion and followed her before deciding to sink her.
Ultimately, this article summarizes that both the US and the USSR agreed to cover up the details of the sinking of both submarines to prevent the outbreak of war. It seems highly likely that this was indeed the case.
It is unlikely that a Soviet sub sank the Scorpion. At the time, Soviet subs were considerably more noisy and slower than American subs. To follow or shadow the Scorpion a Soviet Echo would have had to go at speeds that would have made it easily detectable by the sonar room of the Scorpion. To attack in such a situation would be extremely risky. When a submarine opens its torpedo ports, the noise is loud and distinctive, so the Echo would not have been able to make a "surprise" attack on the Scorpion. Of course, sometimes subs do open their doors at each other as sort of a "threat", just to see what the other guy will do. Nevertheless, if an Echo had been following Scorpion and opened its doors, Scorpion would have reacted in a defensive way.
It is unlikely the Soviet naval command would have ordered their sub to attack the Scorpion, because if the attack failed for some reason then the results would be incalcuable. Even if the attack succeeded, if the United States discovered what happened somehow or if the Scorpion had only been damaged, not destroyed, then the Soviets could have faced severe consequences.
The likelihood is that some accident occurred onboard and sunk the vessel.
There are many types of accidents that can sink a submarine. Virtually any fire is a life-threatening situation because the smoke will rapidly fill the submarine, reducing visibility to zero and asphyxiating anyone who does not have an oxygen tank. A similar kind of problem is a torpedo engine activation or battery fire. The Scorpion carried a lot of battery-powered torpedoes. They can overheat, burst the torpedo casing and start a massive fire. You have heard of laptops catching on fire? Imagine that 10,000 times worse.
(Kind of a joke that my answer, the correct one, gets -1 votes and an answer by someone who knows nothing about submarines gets 15 votes by proposing the ridiculous scenario that a Skate-class vessel sank a Golf II-class vessel by running into it submerged.)