Well, I'd say unless most people say their characters deserve to be there then they don't. Most likely don't go with the though 'yeah, my character deserves to be here' or at least I know my character didn't. Thats why its left open, so you can decide your characters past. You don't have to be innocent, but I can guarantee most people don't come with the approach that their not.
Personally, I hate roleplaying the innocently accused paladin.
Considering where the rest of the game leads me after Helgen, I'm going to say that hardly anyone can be a Paladin. They'd have to basically skip everything, short of getting Ysolda's mammoth tusk, completing the MQ, and wishing Paarthurnax "good luck". Do anything else and you're pretty much a bastard, who deserves an execution, sooner or later.