The title does have other connotations but I have seen that look of "oh no" when someone's dog gets a ground scent, stops, checks it out, drops & then proceeds to roll in it with great enthusiasm.
And no, this activity isn't a learned behaviour, it's inherited with that "canid" or canine gene so it's not restricted to domestic dogs.
Firstly, the coyote in the following photos, is actually in a state of total bliss & is not in anyway, injured. It put its nose to the ground, picked up a scent of some kind, did an about face and sniffed again. Then came the stop, drop & roll. And then it stood up and continued on with that all important pursuit of mice and voles hidden deep in the snow & matted prairie grasses.
This coyote has some quite dark red colouring on its ears, legs and tail and can appear almost fox like (other than its size). I've included a a close up to demonstrate what a stunning example of its species this coyote truly is (Photo #8).