I've never heard of ASCAP going after libraries either. But once they did (assuming it was ASCAP and not some hustler pretending to be an ASCAP enforcer) for the library to ask Mrs. Kate for the letter was reasonable.
The story about ASCAP (again, assuming it was ASCAP) trying to collect a performance license for J.S. Bach's music is even creepier.
My $0.02: People who encounter rude or unreasonable requests from people claiming to be ASCAP enforcers should document the incidents carefully. Note the date and time, get the enforcer's name, and try to get the enforcer to put in writing the claims he is making on ASCAP's behalf. Otherwise ASCAP can simply deny the incident.