I did a little research (should have done it before I posted) and I think I found my answer.
The parking at the cancer center where I go is run by Healthcare Parking Systems. In an interview with the president of the cancer center one of the valet supervisors for HealthCare Parking Systems was quoted as saying:
Healthcare Parking has two models for collecting revenue. The hospital can offer its patients and guests free valet parking, then pay the company on an hourly basis. If there is a charge for parking, Healthcare Parking pays the hospital back a percentage of the parking fee. Malatin said many hospitals have found parking can be a profit center for their operations.
My take is since the center offers "Free Valet Parking" they are paying Healthcare Parking Systems and the patient is not expected to tip.
Thoughts??
David