“most” Ivy schools do not offer the same FA, and Cornell doesn’t offer the same as Princeton or Harvard. They will try to adjust their aid to match P and H, so I think they are afraid you will get an offer from H for $10k more and then they will be expected to adjust their award (upward).
I think the coach has had this happen more than once, that either the school has to match the FA or that the student ends up going to H or P because of the higher FA.