When a prophetic Emperor with a powerful artifact says your character needs to do something, how could they just ignore it if they aren't abnormally dumb, nihilistic, or heartless? Even if you didn't believe his prophecy, the Emperor was just assassinated along with his known heirs, so finding Martin to get the next Emperor on the throne would still be an important task. And since he glued the Amulet of Kings on you, you have to involve yourself since they'll need the Amulet.
My criminal scum couldn't care less about politics and who rules the empire - Uriel or Mariel or anyone at all. She was in prison because she deserved to be there, and got a chance to get out of prison which she eagerly took, and didn't care about anything else but not getting caught again.
Sure, first playthrough pushes the player down the destined hero path, but if you're an adept TES player, you know you always have an option not to be that guy. And even during first playthrough, one must remain very focused and determined to stay on hero path - I for one never managed to do that. In my first Skyrim playthrough, I got distracted from MQ as soon as I arrived to Riverwood general goods store, and didn't get back on track for a loooong time. In my first Oblivion playthrough - same: once I started to talk to people which happened very soon after escaping the prison (Aleswell, Zero Visibility), I got svcked into much more fun and interesting things and completely forgot about MQ, then eventually forced myself to deliver the amulet, fetch a certain someone and escort him to a safe place, and decided that with that my mission is over, apart from closing OB gates near roads and settlements - because I am a responsible citizen and got the know-how and not because I felt god-sent.