hey, you might be right, we have no way of finding out, but I gotta educate you about a more likely scenario. I'll break it down into 2 sections: gill covers allowing stationary breathing, and the actual behavior to do stationary breathing. It is the muscle attached to the gill covers that fans the gills underneath allowing breathing while still. The existence of big pelagic fish such as tuna, dolphin, swordfish, and marlin (whom all have gill covers) suggest that the covered gills are a synapomorphy of osteicthyes (basically means that gill covers are one of the defining traits of the boney fishes, sharks are not boney fishes btw). since it's a synapomorphy, then that means all boney fish have it, regardless of whether they're trying to stay still hiding from sharks or w/e. this concludes the counterargument on gill covers giving pretty much every fish the ability to breath without swimming.
Now to address the second part- simply breathing while staying still is a behavioral adaptation, NOT a physical one. sharks can do this too. wobbegong, whitetip reef, nurse, angel... looking at the original post he asks why the dogfish didn't evolve this ability. obviously sharks can do this (not all), but the ones that did evolve it needed to for some reason... perhaps to hide like you said? who knows? and the dogfish did not need it (as octopus attacks are rare, not that it would've survived the attack either way) as for boney fish, every fish can breathe without moving regardless of whether they need to keep moving or stay still for w/e reason, but only SOME fish (just like SOME sharks) evolved the behavior to breathe without moving while others continue to swim (pelagic fish). so I still stand by my claim that it was luck that the boney fish, with their fancy gill covers, evolved a mechanism that is more suitable to stationary breathing than exposed gill slits (in sharks) are.
I don't know why I wrote all this. sorry I guess. I could've just not responded, it's all speculation anyway- guided speculation at least. I appreciate your thought about it though, keep on thinking :)