Meteor impacts and supervolcanoes seem to be the near-term worst case scenarios, neither which change the state of living on the moon. I don't know that the metaphor of them being under the same roof works.
I know the risks are astronomical (literally), but anything significant enough to alter Earth's mass would also alter the moons orbit.
I just think if we are talking about an extraterrestrial base for the sake of "backing up" the human race then it is prudent to pick a location that isn't in any way dependant on the master copy.
However I appreciate other concerns also take priority as well (cost, practicality, etc) but if the topic were strictly just about backing up humanity then my ideal candidates would be Mars plus some location outside of our solar system. But I'm venturing well into the realm of sci-fi now.