It depends on the geologist's specialty, but the last couple million years are generally considered to be recent. During that time the planet has had a specific climate pattern/cycle and has had more or less the same life, although we seem to be working hard to change both of those.
I didn't see the special but have read a fair amount about it over the years and wonder how long we'd see a bad situation escalating. It would be a nightmare for the world food supply. However, a person's probability of dying in a traffic accident in the US is ~1% and the odds of dying because of a Yellowstone "supervolcano" must be a lot less than that, unless you accidentally hit the gas instead of the brake and drive into a geyser.