If there's really no correlation in SAT scores, I wager that says more about that test than it does about IQ.
Edit for response:
I don't know anything about the MCAT in particular. However I'm confident in saying that the class of people unable to perform well in any sort of test that requires reading and recalling large amounts of information (as learning medicine surely requires, no matter how you structure the education system for it) should find a career outside medicine.
IQ and SAT scores are correlated.
> Psychometricians generally regard IQ tests as having high statistical reliability.[10][65] Reliability represents the measurement consistency of a test.[66] A reliable test produces similar scores upon repetition
https://en.wikipedia.org/wiki/Intelligence_quotient#Reliabil...
> The correlation comes from low scores.
Look at the pictures in this study, that is absolutely not the case, and it will take only a minute to verify.
Frey, M. C., & Detterman, D. K. (2004). Scholastic Assessment or g? Psychological Science, 15(6), 373–378. doi:10.1111/j.0956-7976.2004.00687.x