Totally indulge your player's style of gaming. If they want a good story, give it to them. If they want power, give them that too. If they want intense method-acting, or tactical planning...yes, yes, YES!
I get to pull all the stops. Flashbacks. Cut scenes. And best of all, there is no rail-roading, because the whole point of the game is focusing on the PC's goals.
In return, as a GM I would expect the player to have a juicy background, good grasp of their character's attitude, and a really well done character (rules-wise). Hopefully, I would be involved with the character, and we could come up with custom feats/classes/rules together.
My last word of advice: Take good notes! With one player, inconsistencies are more obvious. They're obviouser.