Is the flying 135? or 91? I think if it's 91 and the PIC is a CFI, and willing to sign your logbook, there is no reason to not log the right seat as dual received/training time. How useful a lot of this sort of time is depends on the situation. Having 300 hours of dual received looks weird in your logbook when you solo, but I don't see any reason not to log it if you can. Just have a good explaination for it.

Backseat time is totally unloggable for your situation.