Yes, that's true, but it's a temporary adjustment, always followed by mass death. This is easily shown in the laboratory -- in the first phase of a multi-species model, one species wipes out all the others. Then the winners turn on themselves.
We are in that temporary zone for quite some time already, and all we need is 100~200 years more until we can get colonies on other planets.
If by some miracle human population was reduced to say 1bln it would make space colonies much less likely, and we'll slowly eat out our petri dish without a chance to enlarge it.
