I know if you want to drive into Burma, you have to own the car outright- you can't still be making payments on it. Is it the same story for Cambodia?

Yes.

You need the log book, in your own name.

Or a letter from the owner giving permission the last time I asked a year ago at aranya phratet

I went in at Arunyaprathaet, and you have to own the vehicle, and have the registration book with you, which has to be in your name, which they keep at the border. Be prepared for a lot of to-ing and fro-ing between the road in, and immigration.