Employment Law Questions? Ask an Employment Lawyer.
Unfortunately, yes they can. The requirement for unemployment is that you must be ready, willing and able to work. Unemployment is intended as a resource to assist people in seeking for work. It is not intended, regrettably, as a short term disability insurance policy.
Chances here are that they want something from your doctor to determine if there is not some work you can do so that they can make a recommendation for work that you can at least be seeking.