I don't think it's an exaggeration, and I don't think it's daft - I think the point of the common quips of the general format "trans 'women' are men", without more context, are almost always (and obviously in this case) simple provocations, intended to disparage and humiliate, in addition to serving as slogans that implicitly support an unstated argument. However, we have no way of knowing which arguments they are supporting, aside from a broad and unnecessarily bitter rejection of the concept of people who feel mentally like a different gender from their biological gender.

So, purely as a random example: One of those unstated arguments is often the "don't let trans women into women's bathrooms" debate. I sympathize greatly with women who don't feel comfortable sharing a bathroom with trans women, and don't think anybody should be put through that (and I also sympathize with the trans woman's side of that problem, and have no good solution to offer to either side, but that's beside the point I'm making), but despite sharing that sympathy, I don't pretend to be unable to recognize hateful versions of that "sympathy" - that would be petty ideology.