You do have to bear in mind that Dumbledore is quite crazy (in a purposeful sort of way). It wouldn't surprise me if he simply found a rock that James Potter had kicked around for a while, and on that basis claimed it was "James's Favorite Rock". Then the rock became a way to force Harry to improve his Transfiguration skills in a huge way.

Also, as rdb notes below, that kind of concentration simply must have bleed over into other types of magic.