They should've asked the question: why is my school billed at a higher rate, than I'm paying at home
You're making an apples to zebras comparison: Residential telephone services are significantly cheaper than business services--such a disparity is by design. The phone company charges more to businesses because they're using the lines to make a profit and the phone company knows that business customers can't live without phone lines.
Without access to another comparably sized organizations business telephone billing records, this would be very tough for the school to even check, if not impossible.
The way to work around this is that there are companies whose entire reason for existence is to analyze telephone bills for businesses, governments, and other organizations. They have access to telephone bills from various customers, and probably would have noticed pretty quickly if such a scheme were in progress.