If he is on the disabled list, then the US Navy will provide benefits. Perhaps if this chap were injured during, say an actual mission into a war zone, rather than joy riding off the California or Florida coast, then perhaps CX may take a different view on subject.
What are the provisions within the contract between the Hornet chap and Cathay for non company flying? I would be my last rupee that CX truly does not care.
But then again, if there were a Sheriff's Lien put on one of CX's toys in JFK, then well... the outcome probably won't be too good.
In any event, hopefully the chap in question gets his FAA medical back and is able to get back into the air or find another position.