No, she did not. The Queen and the Palace made very clear at the time that Diana would remain a member of the royal family and be accorded the precedence she enjoyed during her marriage as the mother of Prince William.
I think the confusion here has to do with a story in one of the many books about Diana that after her divorce most of the royal family cold-shouldered her but Princess Michael, as one royal outsider to another, made a big deal of being friendly with her, going so far as to assure Diana that even though she officially now had to curtsey to Princess Michael, she shouldn't think of actually ever doing so.
Who knows how much truth, if any, there is in that story, but it was definitely in one of the books or articles about Diana.