"Collapse" is maybe hyperbole in this case, if it's building on our own history to extrapolate forward. For us, certain societies have collapsed, and with them have been lost certain practices or technologies, but human civilization as a whole has been largely steady or growing since the agricultural revolution (using population size as a heuristic). There's always the threat of ecological collapse, but that's something that has only happened a few times in the history of life on the planet, and we haven't really faced anything like it before at civilization-wide scale. There's always been another group to move in and take up the abandoned land. Without some major technological breakthroughs, yes, we're likely to face a collapse eventually, but as a biosphere, not merely a civilization. Short of that, people seem to keep on keeping on.

I think the mistake comes from something common to a lot of sci-fi, which is mistaking the scale of a planetary setting. It takes a lot of energy to disrupt life on a global scale (we're managing it, but it's taken hundreds of years). "At some point" is carrying a lot of weight in that observation.