I have not watched the documentary. However, going by Jared Diamond's book of the same name, I would be surprised if it claimed that the Incans capitulated because they believed that the conquistadores were gods. Quoting from the book:
These Spanish victories cannot be written off as due merely to the help of Native American allies, to the psychological novelty of Spanish weapons and horses, or (as is often claimed) to the Incas’ mistaking Spaniards for their returning god Viracocha. The initial successes of both Pizarro and Cortés did attract native allies. However, many of them would not have become allies if they had not already been persuaded, by earlier devastating successes of unassisted Spaniards, that resistance was futile and that they should side with the likely winners.
PBS' transcript of the second episode [PDF] of the series reads:
Inca messenger running to give news to Ataxalpa
Voiceover: News of the godlike strangers on their four-legged animals is taken by royal messenger to the emperor of the Incas, who’s camped in the valley of Cajamarca in northern Peru, guarded by an army of 80,000 men.
Ataxalpa being beautified
Voiceover: Ataxalpa is revered as a living god, a son of the sun itself. He’s in Cajamarca on a religious retreat, giving thanks for a series of recent military triumphs.
Messenger giving Ataxalpa the news
Voiceover: When he hears about the progress of the Spaniards, he chooses not to have them
killed. Instead, he sends back a message. He invites them to join him in Cajamarca, as quickly as possible.
Messenger running to give reply
Efrain Trelles, Historian: Ataxalpa wanted the Spaniards to come to Cajamarca and enter into a trap, and to be sure that they would do so; he played like a psychological game with them, sending presents, asking them to come. Ataxalpa knew that the Spaniards were not gods. The intelligence reports speak of people wearing wool on their faces, like a lamb or like an alpaca, they’re just like an animal. Then they went from one place to the other wearing on top of their heads a little pot that has never been used for cooking.
Wikipedia's entry for Viracocha is another one that questions the White God claim:
Spanish chroniclers from the 16th century claimed that when the conquistadors led by Francisco Pizarro first encountered the Incas they were greeted as Gods, "Viracochas", because their lighter skin resembled their God Viracocha. This story was first reported by Pedro Cieza de León (1553) and later by Pedro Sarmiento de Gamboa. Similar accounts by Spanish chroniclers (e.g. Juan de Betanzos) describe Viracocha as a "White God", often with a beard. The whiteness of Viracocha is however not mentioned in the native authentic legends of the Incas and most modern scholars therefore consider the "White God" story to be post-conquest Spanish invention.
Viracocha, the creator-god of the Incas
If Pizarro and his minions were mistaken for Viracocha, it is usually ascribed to their use of primitive guns with loud bangs (thunder), flashes of gunpowder (lightning) and the accompanying destruction. This might have impressed the natives as being similar to the thunderbolts in Viracocha's hands. The mounted Spaniards also wore shiny steel chain mail and helmets and brandished tough steel swords. These and other factors also mentioned by Diamond could only have aided this notion:
In the Spanish conquest of the Incas, guns played only a minor role. The guns of those times (so-called harquebuses) were difficult to load and fire, and Pizarro had only a dozen of them. They did produce a big psychological effect on those occasions when they managed to fire. Far more important were the Spaniards’ steel swords, lances, and daggers, strong sharp weapons that slaughtered thinly armored Indians. In contrast, Indian blunt clubs, while capable of battering and wounding Spaniards and their horses, rarely succeeded in killing them. The Spaniards’ steel or chain mail armor and, above all, their steel helmets usually provided an effective defense against club blows, while the Indians’ quilted armor offered no protection against steel weapons.