Pretty sure humans caused the extinction of many of the target de-extinction animals. We became insanely good hunters, and killed off just a massive amount of megafauna like mammoths, and then we proceeded to do it to a ton of other species.
I am not so fatalistic about humanity’s environmental impact to just chalk it up to “well, see, mammoths shouldn’t have been so easy for humans to kill and so tasty…” or the same thing applied to any of the more recent species due to habitat loss, etc. (“sorry you can’t thrive in suburbs or clear cut fields, evolution is a b*tch, ain’t she?”)
Humanity’s capacity for higher level reflection is ALSO “natural” in the same sense, so all of these de-extinction projects are equally “natural.”