Yes you can, being imprisoned doesn't make you a bad person at all. It's your decision on making the backstory of our character and you can make your squeaky-clean paladin falsely imprisoned. What we know of the prison start this time, you got captured and imprisoned as you traveled into Skyrim. No one knows why you were captured and imprisoned or why you were going into Skyrim, that's for you to decide and is why the prison start is not only a tradition that is great but also the perfect shoving off point for your character to start off in.
Okay - let's say this: It doesn't allow us to play as characters who have never been to prison. How's that.
Say I'm a magically-inclined thief. I'm stealthy, and capable of becoming Invisible when the odds turns. I've never been arrested, because that would be impossible. Say it would be out of character for my thief to let his guard down long enough to be captured. Then I have to start thinking: "Oh, he meant to be captured, so he can steal something from inside the prison".
OR
I could start out as a free man, penniless for some reason or another, who could make the above-mentioned adventure a part of his in-game escapade, as opposed to having to think around it. I know I'm whining, here, but I can't stress enough how important it is to me to have complete control over my characters situation. If I wind up in jail, I want to do something that makes it happen, you know?