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.
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.