Exempt means not paid hourly. I think you are confusing Exempt with Independent Contractor or something else. An exempt employee can certainly be required to show up for work when needed, be they an oncaller, or a hospital resident, or an attorney litigating in court.

http://www.flsa.com/coverage.html

> The job duties of the traditional "learned professions" are exempt.

> Professionally exempt work means work which is predominantly intellectual, requires specialized education, and involves the exercise of discretion and judgment.