I want to agree with your first point, because I'm confident there are unexaggerated highlights on my resume which would make certain hiring managers skeptical.

I want to agree with your first point, because I'm confident there are unexaggerated highlights on my resume which would make certain hiring managers skeptical. But if we're more charitable about it, they did use the word "clearly"...presumably there is some unconveyed context there about obvious cases of exaggeration. It might not be about claiming something unbelievable so much as it is about claiming something very impressive but not filling in a corresponding amount of detail about it?