Different sizes do look different on different people, people will hold fat in other area, height, how much muscle you have. I don't mean to dissuade you from losing weight at all, but I do think it's why people shouldn't actually compare their body to anyone elses because someone could easily wear a 12 and look different to another person wearing a 12 because of many factors. Sizes are just general like you said, but they aren't an exact science and more than often based on a certain body type and the rest of the us just have to subscribe to it.
I do think Emily squeezes herself into stuff, but also think she does fit some 12 stuff. Even though she's put on weight her belly has remained quite fflat so things would fit differently on her as it does to someone else who may gain weight elsewhere.
Also (and this isn't directed at you) but I think sometimes doctors can just be lil shits. She's free to report her experience of what her doctors said to her, but just because you also happen to be the same clothes size as her, doesn't mean you need to lose weight. Idk why her doctor told her that, but if it makes other people question whether they should lose weight think about how shocking that must have been for her. I don't think she's trying to make anyone feel bad, probably just felt shit that the doc told her that. And if there's one thing influencers love, it's good old attention that says "nooooooooooo, you are perfect"