This might or might not be true. Birds are a good example - they are subject to parasitic mimicry.
One problem that a bird might have is that another bird lays one or more eggs in the first bird's nest. Theoretically, the victim bird will then incubate the egg and potentially feed and rear the nestling as if that nestling were the bird's own child.
There are several points in this process where the victim has the opportunity to defend itself:
- Ducks (at least some kinds) recognize the threat that another duck will lay an egg in their nest, and will fight approaching ducks to prevent them from doing this. But once the parasitic duck manages to get an egg into a victim's nest, the victim is not able to detect the foreign egg, and is stuck incubating and raising the adoptive duckling.
- Some birds learn to recognize their own eggs. If they come home and find a foreign egg in their nest, they will dump that egg onto the ground.
- Birds could theoretically be able to recognize nestlings of their own species. This would not help the ducks from the first example, who are victimized by their own kind. But it would help birds to defend themselves against cuckoos (and similar parasites), who lay their eggs in the nests of other species of bird. I am not aware that any species of bird has actually developed this defense, though I wouldn't be surprised if some have.
Anyway, what's relevant here is that all of these defenses have failed to develop in large numbers of birds that are subject to the relevant pressures. It's definitely possible that the same simple mimicry that worked 100,000 years ago works just as well today. But it's also possible that there's been an arms race.