Very possible. You probably also have some missing trim clips that have been broken off from a previous removal. Mine has 2 missing ones but still sits on there just fine.

I thought mine was out but once I got the DIC out the bulb was fine. It was actually the 2 contact fingers on the bulb housing not making a good connection to the PCB that is on there. Cleaned that up, cleaned the bulb holder contacts and bent them down slightly and reinstalled. Wala. TC bulb works fine.