I agree that how people discuss bodies is an issue, but not for the reasons in the article. The general social attitude very loud in that article is that our bodies are somehow separate from who we are that we can sit with, that we can put a name on them that is separate from us, that our bodies impact how people see us and treat us, but they shouldn't because our bodies aren't really us when, to be a bit pedantic, we are our bodies.
It's easy and useful shorthand for many things to separate our bodies from us as individuals, but I don't experience or exist or feel or think anything without this body, everything I am is this body. I think mind-body dualism that treats us as in our bodies rather than our bodies being us is damaging. I think articles like this rely on the idea that our bodies don't really matter to who we are and it's unfair when everything we view as making someone an individual - their thoughts, ideas, personality are rooted in the body even when we can't see it or what allows that part of them we love to stops working.
I agree that there are issues within many medical communities and rebuilding medical accountability and parts of medical culture would be helpful to everyone, at all sizes. I don't think we're going to get an agreed upon label for every body type as it's partially subjective will help with that. I view myself as bony (and did even after I put on a couple of stone without realizing it a few years ago because the bony parts are what I see first as I spent so many years underweight). I asked someone who is a similar size to the author of the article and was described as lithe and my more muscular parts were pointed out. Someone else would probably have a different way to describe me. I'm around the statistically average height for my sex but would describe myself as short as that's how I feel compared to those around me. Our personal experience and feelings don't have to match how others would see us.
The issues of medical neglect and being able to discuss our experiences are important, but having everyone agree to particular standard terms for body type isn't required for either of those things and isn't helping people working to make a difference on those issues.