I'm not the sharpest crayon in the box, but if I'm reading correctly - you may be misinterpreting her post, and you are in fact both actually agreeing more than disagreeing. Her intent was "If that were true, math majors that are less comfortable....." She was implying that it wasn't true.
But the main point is that the essays aren't a huge differentiator, even at the very top level of applicants/schools. If you look at 50 of them, in reality, you can't separate them into 50 different measurable levels of worthiness. Most are perfectly fine. A handful are memorable. And a handful are pretty bad. In the hypothetical you laid out, with identical candidates in every potential category except a noticeable difference on the essay, you're right - the kids with the better essay should get the spot. It's just not that common an occurrence.