I’m not sure I agree with that. Of course, you should take into account any constructive criticism, complaints or requests, and ask yourself if there might be some truth to them.
But “you come accross as fake” is both vague and personal — and needlessly aggressive for something as benign as lack of follow through. She could also have just asked “Hey, have you sent an email to … ?”.
I don’t think we should encourage that kind of feedback, especially from mentors. I fear it would make insecure new hires even more uncomfortable and insecure.
I also don’t think disagreeing is the same thing as being defensive. I know I’ve been unfairly critical from time to time, and I’m glad I’ve been corrected. Sometimes you just don’t have all the facts in hand.