Sorry for the long delay after that I'm posting, but I didn't have the SoK rules sheet at hand until now.
I think prophecies may be triggered if they are face-up on the deck, no matter how they entered that state.
Usually card effects can't be triggered from out-of-play by the rules, but there are already some cards that supersede this rule. For example Local Sheriff: "Action: Pay 1 to return Local Sheriff to your hand if it entered your discard pile this phase." That effect is implicitly stating that it can be triggered out of the discard pile.
It's the same with prophecies. All their responses read "Response: After X, discard this card from the top of the deck to do Y." So they're also implicitly stating that they're triggerable from out-of-play.
To me, the section in the SoK rules sheet reads like an example for the regular use of prophecies, not like a rule. Especially since it only describes what happens if you use the prophecy's Action, but not what happens if it is face-up on top of the deck through some other way.
But like Penfold said, it can easily go both ways, and Danigral made an excellent explanation for the other way.
I send a rules question to FFG, so we have confirmation.
When a player plays a Prophecy event card from his hand, triggering its Action effect, the card is placed face up on top of his deck. Each Prophecy event then has a triggering condition, which, when met, allows an effect to be triggered from the top of its owner's deck. If an effect would cause the Prophecy event card to move from the top of a player's deck before its Response effect is triggered, the Prophecy card is turned face-down before resolving the effect.