The federal government has a gainsharing program for travelers on official business who get free tickets with frequent flyer miles. Normally you would get zero reimbursement for the zero expense, but gainsharing will reward you for saving the government's money. I don't know the details of how it works, You have to meet certain qualifying requirements.

It makes sense if you had no other use for the free ticket. This way you at least get some reward for using the free ticket to save the employer's money.