A natural predator is incentivized to identify and go after a weak prey animal, b/c it's easier. Maybe this shifts the prey population to be a bit faster, or have sharper reflexes or something. But a modern human hunter may feel drawn to try to take the choicest specimen (e.g. a mature male deer with large antlers), and shoots from a distance, and a bullet moves too fast for the variance in reaction time or running speed of the animals to matter. Do human hunters using modern tech really select for fitness?
I do know that in fisheries around the world, when regulations said that only fish of a given species above a given size could be kept, fish got smaller. I.e. they were "fitter" in the sense of being more likely to be released by a human fisher, but not in the sense of having gained any advantage wrt the natural parts of their ecosystem. There are a lot of fishing competitions where the size of the largest fish trends down over time (and the records were set decades ago) not because individual competitors got worse at fishing, but because we selected against large fish.
I think the most plausible argument for human hunters being a net environmental good is just that in many places the fees associated with hunting licenses are a source of funds for actual conservation work.