I've got a feeling the answer to this is extremely complex. But it's clear to anyone with a fundamental understanding of dogs that the idea of dogs trying to "mask their own scent" contradicts the whole essence of what dogs are. It's really obviously not the case. Other predators DON'T do it, actually bears do, but bears are hardly even predators. What bears have in common with dogs is an extremely sophisticated sense of smell. All signs point to this behaviour serving an intraspecific purpose, that they cover themselves in scents for the benefit of the advanced scenting abilities of their kin. Cat's don't roll in shit, they bury their own shit, and most of them are practically odourless because they are true stealth predators. As if a herd of deer in a field won't be alarmed by the sudden powerful stench of rotting flesh and feces hitting their nostrils? That's a head turner, the thing is dogs don't give a shit, they saunter casually towards a herd in plain sight and watch them bolt, then they analyse their movements for abnormalities, pick out the most vulnerable and run them into exhaustion before tearing them apart. Alternatively they might keep tabs on a moose that lives in their territory for years, smelling where it's chewed grass or browsed on a tree, and smelling it's dead skin cells where it's layed down etc to get a diagnosis on it's condition, once it's teeth start rotting and it starts getting elderly skin diseases and so on they know it's time to strike, but still there's no stealth involved. They know where it's going to be and they mosey on down to engage with it. Frustratingly (because it complicates things and simpletons need simple answers) some dogs do occassionally "stalk" certain kinds of prey, and know to stay downwind of them. I know my dog will stalk wallabies like a cat, and circle downwind from them before charging in. But there's some variables to take into consideration. He's really learnt this from hundreds of failed attempts to course them fairly, also he's of molosser ancestry, and mastiffs are odd canids in many ways, with many cat like traits. For example they lead into engagements with their paws, clasping onto foes and quarry with their forelimbs before biting. Most dogs lead with their mouths, and don't posess the dexterity to grasp anything with their paws. Mastiffs are also explosive like cats, powerful, but lacking the endurance of the classic dog (although still miles ahead of any cat) as well as the pace, so they're more inclined to try and ambush or stalk prey because it's just better odds. I think wolves might stalk jackrabbits and hares, but really this behaviour of covering themselves in stink is just far more significant than any importance canids place on stealth. It just really wouldn't make sense. I'm very confident that dogs roll on carcasses and feces FOR other dogs to notice, why specifically I'm not sure.