There are some schools that don't even require the subject GRE, only the general. Granted, they're not top-20 programs, but still, there's a few out there.
At the end of my REU (which was at a school that is no slouch in math), we had sort of a grad-school primer talk. There was a professor who sat on admission committees that was answering questions, and he had a very poor opinion of the GRE as a predictor for success in grad school -- both the general and subject test. Evidently his opinion was not unique in the department, for the department doesn't require the subject exam for admission.
To echo what owlpride said, I was encouraged by my REU school to get high scores on the general GRE so that I could compete for university-wide fellowships. When the university is comparing biology, sociology, math, etc. majors for fellowships, the general GRE seems to be the only common metric between them.