That is what the show was suggesting, but I don't think it's true.

I don't actually think it's true either, which is why I'm a little miffed that it's what the show implied. Certainly Amy being dead/rejecting him would be a huge fear for Rory. I like your point that the monster perhaps couldn't feed on Rory because he lacked a single guiding faith, even if he wasn't entirely faithless. I wouldn't characterize Rory's feelings for Amy as faith. He sees her faults, and he has on occasion doubted whether she loves him more than the Doctor.