I think the main reason Hawking is saying this is that extinction level events are not rare, and actually quite periodic, sort of like an interstellar bowel movement. The main cause of our extinction would be an asteroid. It doesn't necessarily need to wipe out all of Earth's life, just damage human civilization enough that we can no longer function in the post-impact environment.
Its asteroids that will probably kill us, and no matter where we are on Earth, the likelihood of instantaneous death by asteroid is still the same.