I have a doctorate. A Juris Doctorate to be precise. I don't tell people that or ask them to call me doctor, particularly since lawyers are not normally or traditionally called doctors. They are called many things, but not doctor.
Prior to law school, I had a long successful career in medical research where MDs and PhDs were a dime a dozen. Many were MD/PhDs even. The MDs would sign their names followed by MD. Some PhDs would do that, but not all of them.
If the ticket asked for it, and the lady put down PhD, I would think a customer oriented agent would take the initiative to look at the ticket, note the PhD, and as a courtesy call her Dr. So and So.
Since the agent did not, the lady shouldn't have had a conniption fit over it.
If the ticket did not ask, and the lady had a conniption fit, then she needs a real MD specializing in Psychiatry or something.
As a respected judge once told me when I had too many of the same questions during cross examination, "move on Ms. vagabond, move on."