What could cause a gas fireplace to come on by itself?
Some gas fireplaces with electric start have a thermopile that generates enough electricity to keep the valve open, even if you disconnect the mains electricity. So if the fireplace was on already and you disconnect the main power, I would expect the fire to stay on.

However, starting by itself is not a good thing. I would look at two components: the control board the the thermopile and solenoid connect to, or the remote control receiver. If you do have a remote control receiver, it's easy to eliminate that as the problem because you can just disconnect it. Otherwise, just replace the control board.