If you're out on FMLA you don't get paid. If I have a health issue that prevents me from flying (i.e. Sinuses) but doesn't prevent me from leading an otherwise normal life, you bet your butt I'm going to have a "side job" so I can pay some bills.
The only side jobs this company is concerned with is flying done outside of the company. It's none of their business if I work as a Walmart greeter on my days off.
If he was doing outside flying and lying, well...stupid him.