Three2Tango, I may be in the minority but I don't feel you were in the wrong for asking your coworker about her degree or lack thereof. I think that political correctness is running rampant in today's workplace (not that I am a part of today's workplace, but I know people who are

) so management sort of panicked when she complained that people were wondering about her educational background. Hence the hammer that was dropped on the department.
On the bright side, I think your coworker has answered your initial question!