No. But they can demand that the employee confirm it. Simplest way to clear up misconceptions about HIPAA is to realize that an employer can ask you for a doctor's note to prove that an absence was medically excused. Most people know that, but for some reason there is a disconnect between that reality and what they think they know about HIPAA.
But I don’t think employers are entitled to know the basis of your doctor visit, i.e., your symptoms or diagnosis.