Just out of curiosity, are you living and working in the U.S. or in England? I was just going to say, if you are in England, things may be a little different, with laws and commonplace occurences such as this.
But, if you are in the U.S., then I wholeheartedly agree with the others, they have no right to be putting you in this postion. Well, heck, I was an administrator before I retired and I would never in a hundred years, think of invading a person's privacy like suggesting such a thing. I mean, come on, asking to speak to your doctor? Next, she will be wanting to confide in YOUR lawyer. No, I think fish has a great idea and its thorough and gets you out of the line of fire for now. Cudos to fish!
Please come back and let us know how you make out, OK?
Good luck and God bless.
Lindaloo