I can maybe speak to this because my numbers (3.75/38) are very similar to the postulated numbers OP suggests. I applied in one cycle and had a great cycle. Did that mean that I got into every school? No. Interviewed everywhere? Nope. I didn't even get a secondary at one of the few top 25 schools that screens them. I also got almost universally shutout for interview by mid-tier private schools. It's impossible and would be arrogant to say that it's because of my MCAT, because it is insulting and discounting to those that got interviews.
@gyngyn spoke to this - they didn't feel I was good enough to be accepted/ likely enough to to matriculate to spend an interview slot on me. If any one school can reject you, it is certainly a possibility that more will, and maybe even all of them. I think the best advice to someone already applying is to be genuine and genuinely excited and honored to be given the consideration that an interview is. If it's not time for you to apply yet, then beef up to create a well-rounded application and make sure you are doing activities you are passionate about. Don't worry about doing well hurting you, though. Also, be very sure that if you do have high stats you aren't arrogant. Many of some of the best physicians in the world likely didn't kill their MCAT, so thinking you're better than other people interviewing would be the wrong way to go.
I do think some public, state schools would rather not accept you right away and may put you on hold/waitlist to really gauge your interest before they give an acceptance that likely won't lead to matriculation, though.