http://thevitalounge.net/czech-retailer-lists-prince-of-persia-trilogy-for-ps-vita/ Another "rumor" that's probably false. I hope its true, I bought the Collection on PS3 but never got past the first game. Would enjoy getting the chance to play Sands of Time on the go.
Probably false, as you say. Although, Forgotten Sands is actually a pretty decent game, and it's on the PSP.
The fact that the PSP has the 2nd and 3rd game is probably the biggest red light warning sign to me that this is unlikely to ever happen. This and the Ico/SotC Collection are the only 2 left that I'd like to see on the Vita. Although I'd be more than slightly concerned about their ability to run at a decent framerate/resolution.