It may not be "multi-user" by that definition but the exact definition of "multi-user" isn't really that interesting for the actual argument, is it?
Isn't the point that as soon as soon as there are multiple users (no matter if they are logged in using a system account or accessing the system through some other means, eg HTTP, authenticated in some way or even anonymously), there would be a chance that one user's data (or data "belonging to the system") could leak into a file which will be accessible by another user.
So in the case of the the system crashing, a file publicly available on the web, or some logged in user(s), might end up containing anything that has previously been deallocated if that file was being modified, be it by the site administrator, or by a random user on a site where you can for instance upload an image to include in your content.
I would think this definitely falls within the "common usage"-realm for Linux systems and that whoever made the argument may not have really thought it through.
(Or I'm just not understanding in what scenarios something like this could actually happen.)