It's really not that clear cut. To do what you propose, you either have to set up an identical staging environment, or you have to set up a local environment that mimics (and stays in sync with!) the production environment. For a tiny site that sees <100 people a day, where the potential damage of a mistake is absurdly low (so what if 5 people see the broken version while you make corrections?) it's not necessarily worth the additional hassle.

This all depends on what kind of site it is, of course, but in the context of what he's saying, it makes sense.