Arena: You're still a prisoner. Just because you're the prisoner of the enemy doesn't mean you're NOT a prisoner.
Daggerfall: Yes, you end up in Daggerfall itself when your ship wrecks, but it states that you were released from prison to do a task for the emperor which required you to go to Daggerfall. Starting zone not withstanding, it clearly states you were a prisoner.
Morrowind: yes, you get out of a boat... A PRISON BOAT. You were arrested and sentenced to exile on Vvardenfell. Kinda like how the British used to send undesirables to Australia.
Note that I said you start as a PRISONER. Not IN A PRISON.
Of course but than again, I see it as this: the PC is a prisoner to the Main Quest and how one follow it, but even then, the intro isn't that of "prisoner".
Arena: One is stuck in a hell hole left for dead. That not being a prisoner, that just being doom to die.
Daggerfall: That just one of the template that the background is offer. One get that if one is more "stealth" like build. I got the Mage Template with the wand stopping the bandit. Even than, the template is easily forgettable and the real intro is simply just the Emperor saying ya his friend and one go to Daggerfall. No prisoner here.
Morrowind: Who say that I was prisoner and really I am agent to the Blade with a low profile? The intro is short and forgetable when one get out of the office, Hell, I can see this as a cheap fare for any immigrant to travel to Morrowind and all destiny is really handed to Jiub.