I think perhaps what was meant was that if the average annual temperature were to change by one degree either way we'd suffer those consequences. If the Earth were nearer the Sun at the closest point in its orbit, or further at its most distant point, then the average annual temperature would change.
However, I doubt the range is that small. I recall reading that when Greenland was "green" the Vikings settled it, then the "Little Ice Age" descended on them and the average annual temperature dropped by 1/2 degree and Greenland was covered by ice, crops failed, and they all starved.
So, it doesn't take much of a change to cause trouble.
However, if the temperature is not too extreme for life to form in the first place, it's probably adaptable enough to survive at average annual temperatures within a few degrees of what we experience here.