I've never seen one credible argument from anyone that invalidates the fact that the camera (or at least the glass that one chooses to mount upon it) does really fricking matter.
For example, I use myself. I was shooting a lot of street, mostly subway and urban stuff, with a Minolta P&S. The minute I upgraded to a DSLR, my photos improved tenfold. My compositional skills didn't improve. My ability to SEE (note the caps? Just like Ken used!) didn't change. My ability to capture, however, improved with the improvement of the camera.
In the article Suhit quoted, there's this:
Photography is both an art and a craft.
That is the absolute 100% truth of the whole thing. The art is knowing what to do. The craft is having tools capable of doing it. If the tools didn't matter, Ken wouldn't own so many cameras, he'd carry his beloved Casio P&S with him everywhere and call it a day.
But he doesn't.
Because the camera does matter.