It's merely a shorthand way of saying "many people have a cognitive bias that humans are more 'special' than they actually are

This statement implies that humans can be more or less special "actually", as if it were a matter of fact, of objective reality.

That is not true, however. Humans are special in the same way a roast is tasty or a host charming. It is entirely in the eye of the beholder, it's a subjective opinion and as such there is no "actually" about it.

Your point is equivalent to saying "many people have a cognitive bias that roses are more 'pretty' than they actually are".