Just my two cents worth: I am finishing up my "consolation" MA and going into my third application season to Ph.D. programs. I scored in the 99% on the old verbal (790) and 98% on the subject test, and I really don't think these figured much in any of my acceptances or rejections. I know my scores are much higher than many students accepted into the Ph.D. program at my current school, so clearly they are not a primary factor in admission.
(I also got a low [4] score on the writing, I think because I just couldn't bring myself to write a formulaic, five-paragraph essay. Silly me!).
I think schools want to see solid, but not necessarily astronomical, scores as confirmation that you didn't have your brother write your recommendations, but I think the importance of the GRE tends to be distorted by us nervous applicants wanting something tangible to cling to in the application process. Programs want flawless and compelling writing samples and SoPs, as well as excellent LoRs, so they can be confident that their chosen few will flourish in their program. Concentrate on your SoPs and your writing samples, they really are much more important.
I think that programs are reluctant to publish minimum scores simply because they do not base their decisions to any great degree on these scores. The scores serve as supplemental information used to round out the picture of the applicant. Otherwise, admissions would be very easy since schools would simply accept those with the highest scores, and no one with scores under, say, the 97th %ile would ever get in anywhere, which we know isn't the case.