We think an employee qualifies for FMLA, should we request certification?

Q. When an employee requesting FMLA submits vague provider documentation regarding their serious health condition but the employer has knowledge that the condition would qualify under FMLA as well as ADA, should the employer request written verification from the provider?  And, how much information should HR share with the employee's supervisor without violating the employee's request for privacy? – Kathryn, NY