It's truely amazing that there haven't been any mass extinctions.
There have been, no one says that a species can adapt to a volcanic eruption or a meteor (nor can they mutate themeselves out of it!). However, they can indeed survive through the more normal environmental changes cited in the post you responded to - without mutation - because there is simply no time for them to 'evolve' fast enough to meet these changes. Besides, these environmental changes do not give thousands or millions of years of warning so that the species can get 'ready'.