Carlsen has already played about twice as many official games as Fischer played in his entire career. Part of the great tragedy of Fischer is that there are so few games available. It's possible that Fischer could have improved even more, but he chose not to.
I agree with just about everything PFren has said in this thread regarding the relative strength of Carlsen and Fischer. Fischer was truly great. He inspired future generations, including Kasparov and Carlsen. Carlsen has committed to memory just about every important game Fischer ever played.
Kasparov and Carlsen are better than Fischer in large measure because they stand on the shoulder of giants, including Fischer himself. They studied and learned from Fischer's games. But yes, they have indeed surpassed Fischer at his best.
"Carlsen is the least computer dependent top player currently (together with Peter Svidler). He is the world's #1 simply because of his phenomenal positional understanding, and awesome fighting spirit."
C'mon every strong player today has relied on computers to one extent or another. If we could identify the GM who uses them the least it is still unarguable that that person uses them more than EVERY GM in 1972. That's because no one used them in 1972.