I co-supervised a British PhD student once who did his PhD at a Spanish university. Not only was he a native speaker, but he also wrote very clear - no passive sentences, clear structure in thinking and writing, very good. He had a paper reviewed by someone who only saw his university on that paper (blind review) and wrote 'paper could do with review by a native speaker'. Why? No idea. I knew who the reviewer was (small world) and he wasn't even a native speaker himself.

My theory: when you ask someone to correct language, and they know the author isn't a native speaker, they'll nitpick on things that native speakers wouldn't be corrected on; but the corrections will be much more about the idiosyncrasies of the corrector than the level of the author (when that author has reached a certain level of proficiency of course).