As much as this advice is right on, I'd simply say that my intuition is that GRE scores matter most when it comes to university funding sources. For better or worse (and I think for Far Far worse!) the GRE is considered something of an objective criteria wherein a department chair can take a student's information to a dean and say, 'look, this guy/gal scored in the 99th percentile in his Algebra II for adults exam!' So, it seems to me that when a faculty member tells a prospective student that they need to do well on the GRE they are in no way saying that if one does well on the GRE they would be delighted to advise them, but, if not, they wouldn't. They are simply saying that if you are an otherwise attractive candidate for admission, high GRE scores might bump you into the 'accept' category due to the fact that it may be easier to make a case for funding on your behalf.
On this, I've often thought that any department/div. school that has anything close to a 700 cut off (officially or not) should promise to have one or two senior faculty members take the exam every year and then publish their results on their webpages. Wouldn't those results be fascinating?