This is one of those spirals that some people just have to go down. Either the person is lying to the AGM or the person is putting the company in danger of increased risk of workers' comp claims or, even, an OSHA problem, depending on what the supervisor actually supervises.
Take a look at this discussion on ADA and forcing a person to take a physical: http://community.blr.com/hr/forums/thread/4954.aspx
If this person supervises something that could put others in danger or if their own performance has gone down significantly (to the point that it meets the harming company efficiency threshold), it's a no-brainer: send her out for a fitness for duty test and check with your attorney about HIPAA/ADA/state privacy obligations before you inform the healthcare provider that the person has claimed to be told not to work because of a brain tumor problem and that the person has had surgery in the past for a brain tumor.
You can tell the individual that they may not return to work without a work authorization from a doctor. When the person comes with that note, probably from a different provider, you then ask them why they claimed to be advised not to come to work. If they are defiant and make it clear they're trying to game the system, go down the path of asking them why they would provide a false or misinformed medical opinion to the Company and see if this person will step over the line into the realm of breaching your policies on providing false information. Call your attorney for options and direction while the person is out getting a return to work authorization. If they say that it's all better now, and your attorney has nothing better for you, at least you've covered your company as well as you can. Document, document, document.