Wake up pal, yes it IS their fault for placing the booking without paying for an early arrival and late departure. They booked it to save as much money as they could at his expense figuring that he would be keen as mustard to join and a little inconvienience to him won't matter.
They don't give a rats he flew in Economy all night from Europe and was made to wait for a room and then check out way before his flight later on.
They could have done the right thing, after all we book hundreds of hotel rooms for crew each and every day based on our roster and this is not a new concept.