That's just as unbalanced a view as "endangered species may never go extinct". The difference is whether they go extinct because of maladaptation to the natural environment or because of maladaptation to human influence on the natural environment. No reasonable person would argue against the first thing, but many argue against the second thing.
Are humans not part of the natural environment?
It's a bit disingenuous to call extinction caused by human activity "nature's hygiene process".