I never liked that whole 3 years comment. Not saying Kirk wouldn't be intelligent enough to do it in 3. But you don't just need intelligence, you need to actually take a lot more courses in a shorter amount of time. Does Kirk in the movie seem like the type of guy to spend almost all his evenings in class? Furthermore, even if he is really smart, Starfleet is obviously really really hard to get through. So it kind of makes it a little unlikely unless you're someone of Spock's caliber.
He has a genius level intellect according to Pike. Apparently tests were given.