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Far from unlikely, I have seen government-operated metropolitan-scale networks that allocated extravagantly in their early days and ended up using all of RFC1918 space, being unable to renumber (because change in government systems is Too Hard) and moving on to more esoteric non-globally-routable space.

For those intrigued as to what those addresses might've been, have a read of Bill Manning's roll up of the special case IP allocations: https://tools.ietf.org/html/draft-manning-dsua-08

Could just as easily be 10/8 nationally, 172.16/16 within the school board, 192.168/16 within the school or something equally innocuous.

It's hard to be sure of anything there.