Right, they don't look closed. Sometimes they can get it tossed totally backwards, onto their back! How? Maybe we need to see a naked chicken doing itThat doesn't show the feet much, but they don't look closed. Fun to watch though.

I did see here that she kicked debris up between her body and her wing, then later turned to the side and flapped it further onto her back. Cool.
Could they be using the top of their feet?
Also, the vocalizations sound really like a prehistoric dinosaur movie! I wonder if the feathered dinosaurs did any dustbathing?