You keep contact with both. Pay the money to the school, but get the feedback directly from the student. The school would have to collude with the student to claim that school fees are paid when they actually aren't.

I mean sure, but at some point you have to trust someone. Take it far back enough and we could argue you also have to trust the banks used for the transaction.

The institution has more eyes on it than an individual—be it journalists, the government, concerned citizens, even the students themselves—and is thus more likely to be caught in fowl play.