There's no rule that says the biosphere has to be resilient in every dimension we might push on it. If the biosphere has been stressed in a particular way and life (animal and mammalian life, specifically) rebounded, that does not mean the biosphere is resilient to any other kind of stressor, and it's only mostly assured that it's resilient to that particular one because of empirical evidence. We don't have models accurate enough to confirm your suspicions about the hardiness of the biosphere. There may be an attractor to current life-supporting conditions even under a broad range of stressors, but if human progress is adding an additional stressor (that we may not even recognize), we could be screwed.