I have seven kids, four have been through the process.
I have a couple of thoughts, but remember nobody knows your kid better then you do, and nobody loves him like you do, so take all advice with a grain of salt.
First: SAT scores are really, really important. The college admission process is nothing like they make it out to be, it is, fundamentally, a quantitative phenomenon of SAT+GPA+high school reputation (which is a fudge factor). Does not apply to minorities, obviously.
Second: SAT prep really, really works. Depending on your goals, pay for professional help if you can get it nearby. A good SAT course of at least eight weeks duration, twice a week with homework, should raise a kid’s combo score by 250 points.
But, third: Your son’s (and everyone’s) “cold” SAT score is a highly accurate reflection of where a student is really at. The fact that you can turn a 960 into a 1200 DOES NOT MEAN that your son would be happy at a school with a median white SAT of 1200 (except for getting the letter, that makes everybody happy).
To summarize: You can definitely raise your SAT score with prep. Since “America’s Best High Schools™” all devote at least a year to test prep before the PSAT (that’s how they get to be “ABHS”), a higher score will neutralize coming from a “non-top” high school. But, going away to college and being in over your head is a really, really sh*tty way to spend your 18th year, and can lead to premature discontinuation of education. You should definitely be looking at schools with medians in the 950-1050 range, as well as schools with higher means.
And, sorry, I skipped over that part about medical school.
I would never tell a HS senior that they couldn’t do it. I had a 3.0 HS GPA and I did it (I was lucky a bit, applied to 13 med schools, got accepted at 2), BUT, I had very high SAT scores which predict MCAT scores pretty well.
You have to weigh the “If you want it, go for it” feeling with the probable outcome, which is a crash somewhere between second semester Inorganic Chemistry and first semester Organic, maybe a dropout and a least a change of major. How your kid would handle that, I can’t say.