So, they are highlighting some subtle difference between saying -
Amanda, who lives in New York
and Mark who doesn't (without the comma)?
Frankly I'd say that is a very obscure piece of nitpicking, rather than being about the proper use of grammar. It's the kind of thing that gives pedants a bad name!
Anyone who worded that sentence in that way, in the expectation of communicating accurately with other people, is an idiot. Which entirely goes against the reasons why some of us think that grammar matters. The point is that properly constructed sentences make sense and don't leave ambiguity about what you mean (except where that is your intention).