Thanks for the thoughts.
I did call my dealer and spoke to the service department - they said no problem putting a hitch on the Camry Hybrid. They also said it would do nothing to the warranty. Of course this is now.

I don't intend to actually "tow" with the hitch so I didn't ask about that issue.
Uhaul actually list the Camry Hybrid specifically so the hitch should work just fine. I'd much rather a hitch then scratching up my paint with a trunk rack!