I'm not sure about the PS2 version, yet (I don't own THAT), but as far as the PC version goes, all that stuff about it being a "full game" is a lie.
To play Ambition of Illuminus (AoI), you don't need to own PSU, first -- THAT is correct..
..By full game, you think it means you get to play as Ethan in one episode, and then, play your own character in the 2nd offline, and the 3rd in Network Mode, right?
They took the Ethan story OUT, and all of the Episode 2 stories that were online until AoI came out make up AoI's story mode. Basically, the only thing you transfer from PSU are your characters from Extra Mode. Your Extra Mode character from PSU is what you play as in AoI. X_X
So, what does that mean?
That means that, for whatever reason, if you ever wanted to play Ethan's story again, you'd need to hold on to your copy of PSU and download it into your comp. Basically, you have 14 gigs of data of two different games that should've been just one, but for whatever stupid reason, ISN'T.