Correct.

I also believe that one of the criteria for a binary planet is that the barycenter is outside either body. Like Pluto/Charon.

I mean, sure, but that'd be like saying I'm pulling the earth towards me when I jump.

Pluto and it's biggest moon Charon about for the very center outside of each other. This means that you could build a space elevator directly between the surface of each of them and it would rotate around that point since they're also tightly locked.

Asteroids everything does to some degree even if miniscule I'd assume.