There is a difference between trying to prove you're the best and trying to win as much as possible. I don't think AC has anything left to prove. He proved this year that he's very far from past it, and it makes sense he wants a new challenge. AC announced he was going to do the Giro even before the parcours of the Giro and the Tour came out and before all the others announced to leave the Giro for what it is. We shouldn´t expect him to pass the Giro, which he agreed to ride with his own team and with the Giro organisation (not to mention that he loves it) for a high variance ****ing contest in the Tour, which he still do anyway.
About Nibali, I think I've said that he won because his main rivals crashed out. I think he could dominate so much (winning isn't dominating), because he faced weak competition that didn't even bother to follow him at times. Do we know what would've happened had AC stayed on his bike, no, but I think it's a pretty good guess he was the better climber and I like to think he could've taken back all that time. Anyway, most of that talk was about who was the best rider of the year, not about who won the Tour de France or who won the Giro. A Giro win is a Giro win and a Tour win is a Tour win, no matter the competition. It does have influence over who you can rate the best of the year, however.
The Tour is not necessarily the best race. It is the most important one and I think its the most overrated one. The Tour has the most importance because of it's history and because of it's time slot in July, when the people have their vacation and when theres not much other sport going usually (it barely clashes with Wimbledon, EC or WC soccer). Winning the Tour does not make you the best rider, it makes you the most marketable rider.
Oh, and evidently no to the last part