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In my limited experience, roosters don't cause bare backs, but take the blame a lot. They may break feathers and pull some out at the neck, but they aren't pickers, they just want to mate. The other hens are the ones who pick - hence the term "hen-pecked". It is a bad habit that spreads. IMO it may start when the rooster breaks the feathers exposing the fuzzy underfluff and that looks interesting to peck.
If these birds have some kind of infestation, then that may be causing them to pick. The RIR sounds like the chickens I visited at a friend's house the other day. If they were bare and red then they have something wrong. Mites, fleas, skin infection... something. Shame on them for having them in the petting area! I hope you washed your shoes before entering your own yard with your chickens!!
Ugh! It is upsetting that people just keep their chickens like that. It is gross, first of all, and unfair to those birds. If they are going to be "kept", then they should be cared for. Sheesh!