They didn't say that you're in prison for being a Dragonborn, I guess someone misinterpreted someone elses post and everyone just went with it from there... I'll research just to be sure.
Todd spoke about being a prisoner in a podcast-
32:42 Why do characters always start as a prisoner?
"It started that way in arena. We did it again in Morrowind, then Oblivion. It's sort of become a tradition. We like this idea that there's a little bit of conflict in the beginning with you being a prisoner, and we never say why. So you immediately in your head tell a story of why you're in prison to yourself. I kind of like that about it. It's part tradition, and part it lets you in your head tell a quick little story to yourself."
As for the Dragonborn thing, it more of a spoiler, but not anything I'd consider a major spoiler-
Spoiler When you start off with your character he doesn't know that he's dragonborn.
"Correct."
"He does find out. There's an event that happens with a dragon, where you find out you're dragonborn. I think for anybody listening, it won't matter, 'cause they know."
"The greybeards, the guys who live up on the throat of the world, who are the masters of the voice, they find out about this fairly quickly, and they shout your name. They shout Dovahkiin to the wind, and it kind of rumbles through the world. The mountains shake when they call you. And you think 'what was that,' and someone says 'that was the greybeards calling you. To walk the 7,000 steps up the throat of the world to meet them.'"
"I have been promised 7,000 steps, and I am going to count them. Our world artists are amazing. We have just an amazing team, and they put so much detail in the world, so they didn't blink when I said 'it MUST HAVE 7,000 steps. When you look at all the stuff we have in the world, 7,000 steps obviously is not that hard."
As for how my first character got into prison in Skryim, he's an adventurous youth. A little too adventurous. He saw a dragon and thought it'd be smart to mount it. So he waited until it flew near a high peak and he jumped onto its back. The dragon, pretty pissed that something is on its back, tried getting him off his back, but to no avail. My character is pretty nimble for someone his size. While he was busy trying to get my character off his back, he crashed through a tower at a funny angle, broke his neck, and continued to speed forward (curse you momentum!) until he finally met the ground....and about a dozen villagers and a shop.
Guess they didn't take to kindly to my characters fun....