A telephone company worker got married on a day she was supposed to use approved medical leave for migraines. Another employee, who took leave because of an anxiety disorder, played drums in a band on the Fourth of July. A flight paramedic attended three air shows over 12 weeks of baby-bonding leave.

All of these workers were fired for misusing leave. All accused their employers of violating the Family and Medical Leave Act. And they all lost in court.

That’s because the companies showed they had an “honest belief” that FMLA abuse was occurring—a powerful if rarely used defense that’s...