Yes, dead critters, or live ones, can be hard or even impossible to find when obscured, as I noted. And "obscured" is as simple as not visible in the line of sight, like when lying in grass taller than the carcass.
I am aware that an animal can be seen with thermal but not recognized, at least until it moves. But eventually it is going to move, and as I wrote, it will be movement that reveals it. Your cottontail rock hopping away, for example.
Here, especially just after sunset on a sunny warmish or hot day, a critter just inside or outside of a tree line or fence row with brush at the base can be hard to distinguish because of the strong thermal returns from the brush and any bare branches. Particularly if the tree line faces toward the west.
Here we have no issue spotting skunks though they appear smaller through the thermal at first glance than they do through NV or in a flashlight beam, but at shorter ranges close examination with the thermal has revealed a larger profile with little differentiation between some backgrounds and the outer hair and tail. IIRC, their faces and anuses always stand out, and I think their feet, when the grass/crop/dirt don't obscure them. I will pay greater attention when I see one this weekend when I'm out predator hunting.
As far as a dead hog or other critter lying fully exposed to thermal but difficult or impossible to distinguish from rocks, where I have been hunting we don't have rocks, but not too far we have mountains and short of the mountains is cattle country where there are many rocks and rock outcroppings protruding through the pastures and I can easily imagine the situation. Clearly, the more rocks the more checking you would have to do, but eventually, if you check out all of the thermal returns, you will recover your dead hog.
I certainly agree that any animal that is completely obscured is not going to be detected by thermal, or NV, or MK I eyeballs and a spotlight. Short of being completely obscured an animal is detectable with thermal - in fact is already detected if there is a thermal return, though it might take some patience or some changing of aspect to recognize it. That cannot be said of NV or even MK I's and a spotlight.
JPK