Of course it isn’t "free." Someone is paying the valets, the valet company, the insurance, and paying for the parking space where the cars are going. It is "free" to the parker.
When you read the article, you find that the hospital, in this case, understands. They used the term "complimentary parking," and are promoting this as another service offered visitors and patients at the hospital.
The hospital is in competition with other hospitals in the area and wants to make the experience as good as possible under difficult circumstances. The Valet program is a good idea. I’m sure that folks visiting me during my recent stay would have loved to have their car’s handled by a valet, particularly at no cost to them.
However, I don’t think that people expect it to be free, and I would suggest that the hospital charge something, if only a minimal amount. That will most likely flush out the ones who would take advantage of the program.
But there you go.