I'm not sure the quoted statement is true. Proofreading like "point to problems in the text", if you fix the problems yourself and don't copy-paste the solutions given to you, should still be safe, shouldn't it? So, human-written text should not be falsely flagged if you use LLM for proofreading.
And if you copy-paste the answers from LLM, I think it's only fair the end result gets flagged. You're not writing it yourself.