Yes, you were still a prisoner in Arena though. Just because you weren't in prison for picking up a zero value spoon doesn't mean your any less of a prisoner. Also, Morrowind your a prisoner but are released right off the bat. As for Battlespire and Redguard, you weren't a prisoner but they were also not the "main" elderscrolls.
I play the game for a month and I can tell ya the intro isn't a prison at all for Arena. As rabish12 said, the PC was put in the dungeon full of treasure and goblins just because the Last boss does not like ya, not to mention it is not really a prison in a sense as there is no other "prisoner" or "guards" or and jail system like that. The PC was left there to die.
It never says that you have a criminal background, that's the great thing about it. TES found a formula for the perfect beginning, the second formula for the perfect beginning that makes it where you can do anything you want without people saying "But that doesn't make sense". The original formula is "A long, long time ago in a galaxy far, far away." allowed for complete freedom and the fact that you start as a prisoner and know one knows why your in prison, even you means that you can start from scratch without being evil or good. For all you know they put you in prison after finding you passed out on the street thinking you were drunk and all that had happened is you had passed out from some unknown trauma and you got amnesia!
Being in a Prison Cell is more than enough to screw up the mind of "not" being convect to begin with. Even with no "crime" history, one have to make up crap why ya there, which in my opinion, is horribad and that the intro could been done better with a much higher dignity. Oh, and I am not a drinker.
But you were sent there by the Emperor if I remember correctly and you had been established as a trusted friend of his. Do you not think that is a fairly well defined past? Or do you feel that the video and whatnot was short enough to ignore for the sake of RPing? If that is the case you could do that in Oblivion as well by saving at the sewer exit and then as far as I am concerned, I was never in jail.
Daggerfall's movie intro is definitely more open compare to all the TES so far and what lead to that point can go as far as ya being an honor guest or ya were partying with him earlier that day (these are from the preseted intro given). The "saving at the sewer exit" is such a horrible way of siding with the "prison intro.