This logic does not necessitate Mars ever being more habitable than Earth. Imagine one of the countless doomsday scenarios - a large asteroid impact. What kills you is not necessarily the asteroid, but it flinging debris into the sky that blots out the sun, not only creating a massive cold, but also rapidly killing all plants which starts a rapid series of extinction events on up the food chain.

If that happened Earth itself would still, even during the extinction event, be a dramatically more pleasant place than Mars. But nonetheless that event would kill off the overwhelming majority of people on Earth, and very possibly 100%, because it's such a significant change from the status quo we expect to continue on Earth. But having a parallel society or societies would ensure that even in the 100% scenario, life could get back up and organized relatively quickly. And even in the "only" 99% of people killed scenario, the outside help could help to reestablish order and kickstart society.