There was no issue over her title. As a divorcee, she was automatically entitled to use the style of "Princess of Wales" until she remarried. The real issue was her royal rank as HRH, which she voluntarily offered to relinquish early on in a meeting with The Queen and Robin Janvrin.
Later, she decided she wanted to keep it after all (remember Sarah, Duchess of York had also finalized her divorce terms at the time) to ensure her position as the mother of a future king. The Queen and Prince Charles were willing to compromise and offered being created "HRH Princess Diana" in her own right, but she pushed for "HRH Diana, Princess of Wales" instead, which was totally inappropriate for a former wife.
After reaching agreement on all the other issues, Diana telephoned The Queen to ask if she could remain HRH. The Queen said no.