Having interviewed maths applicants for Oxford, I don't think it's just corruption or biases - there are just more really bright students that you have places for and have to reject some people! We all tried really hard not be biased but I don't think there is any way to guarantee that you aren't somehow, however hard you try.

It's very hard to predict from a half hour interview precisely who will do well in future, and in fact some people might do better having gone to other universities. Oxford and Cambridge aren't the best choice for everybody - I'm sure being a bigger fish in a smaller pond suits some people better.