This is a fascinating example of a linguistic shibboleth in English society: teaching that using certain expressions defines you as well-bred, educated, etc etc.....so instead of having the confidence to think the language through, a knee-jerk reaction to 'me' whispers in the background that saying 'me' in this context is....well.....common.
I get metal images of doilies, cakestands, prickly clothes and bakelite telephones just thinking about it. It's a me thing.