Not sure about the systems you maintain, but mine page for false positives all the time. They're annoying, sometimes they wake me up, but in general they're not a big deal.

A false positive from a medical test is much more costly, both in money for a doctor (or doctor's staff member's) time, and anxiety for the patient.

That said, your brother's case makes some sense. It's targeted, and I imagine the action you want to take after getting an alert would be pretty well defined.