Yes the integrator is responsible for pushing to the central ('release') repo. We have only a few integrators per repo (we have a corporate setup).
I also agree with most of what Ingo says, but AFAIC there's not much difference. The thing is though that we have just switched over to Git and the devs have to get used to many things. Many devs are not of Linux kernel quality and do not develop their features in an ordely and structured fashion. Rebasing gives them the tool to clean up their mess before submitting it for review and integration.
Note that we still require small commits that build towards the feature, etc etc.
Once everybody is properly accustomed to Git and what it can do we can start to think about other policies :-)