This guy is obviously very intelligent, but because the UK is so specialised at university level he would have only been judged on his ability in subjects relevant to his chosen course (he applied to Oxford for Maths). The tutors want the people who will be the best at their chosen subject, not necessarily those who can get A*s in loads of subjects but not truly excel at one. It is quite conceivable that he did not do too well on the MAT/interview and was edged out by better candidates for maths specifically. Indeed, the fact that he is leaning towards Chemistry now as his major for Stanford perhaps puts some doubt on his commitment to Mathematics as a degree subject.
It's not surprising that the top US unis snapped him up though, given that you don't apply for a specific subject and their focus is much more broad: his impressive subject mix and high attainment across the board is probably what attracted them.
At any rate, I'm sure he'll do well at Stanford and wish him all the best.