I don't really buy that. Unless you're at the C-level, you know nothing about how the person working next to you quit their previous job.
The only exception being them volunteering such information, but even in that case an abrupt notice of termination paints the story teller in a positive light of him (finally) seeing the light and moving away from sinking ship that is her old job to the unbridled rocketship of opportunities and awesomeness that is her new job.
Since when is quitting damaging? Obviously there are a handful of extenuating circumstances where you really leave an employer out to dry, but in the general case there's nothing wrong with quitting a job.
The only exception being them volunteering such information, but even in that case an abrupt notice of termination paints the story teller in a positive light of him (finally) seeing the light and moving away from sinking ship that is her old job to the unbridled rocketship of opportunities and awesomeness that is her new job.