I'm not really sure as to what you mean by NCAA-style teams. Stanford is actually the school that the sports world points to as the shinning example of excellence in sports not interfering with excellence in academics. In fact last year Stanford Basketball went to the sweet 16 in the NCAA tournament. Before his career as pro-quarterback John Elway was a Stanford student-athlete. Furthermore every university in the academically vaulted Ivy league is also a member of the NCAA Division I.
Tell you what, though: when I chose between Stanford with its athletic program and Caltech with its lack thereof, I considered the athletics a knock against Stanford. I ultimately chose Stanford, but despite the athletics, not because of them.