The question wasn't "Who was the best player for the Spurs in the 2013 Finals?" That's how you're answering it, because you're looking at what actually happened and picking from that. But what actually happened is that the Spurs lost, and the loser doesn't get a fMVP. So at some point, you have to change the timeline. If you change it at Ray Allen's shot in Game Six or Duncan's miss in Game Seven, you can make a strong case for Duncan. If you play those two games over again, then it opens up, because Green, Duncan and Parker all had cases going into that game. Duncan pulled away in the real world, because the Heat changed their entire defense to stop Green from shooting. It's not surprising that Tim had his two best scoring games once he became a lower priority to check. But if the Heat just didn't do that, and Game Six was just another game in the series that the Spurs won, Green had the storyline and the numbers to get the award.
And you think that's silly, but then the next two fMVPs were also awarded to role-players as opposed to the stars on their teams, so. Like it or not, fMVP isn't the same thing as "best player". It's something voted on by the media, and the "storylines" you mock matter.