I'm thinking your parents are probably right and the boredom is resulting in feather picking. Have you considered expanding their run, perhaps with portable poultry netting? Do they have a dust bathing area?
Yes, it can. If they have a bad infestation of mites you'd have them crawling all over you when you visit the coop and you'd see them all over their eggs.
What are the dimensions of the coop and run?
Yeah, I'd have to go with my dog. And if my house was burning down the non-living thing I'd take is my backup hard drive with all my photos and other memories on it.
Finally nearing the end of my barn to coop conversion! I stained the trim and patched the roof last night.
The view of the chicken yard from the roof of the coop is wonderful! :D
Looking back at photos mine didn't have the curled feathers as a pullet but it appears she had them at about a year old. I guess I didn't notice them back then.