Was this anywhere near the emergency entrance for the hospital? It makes sense to minimize traffic there for ambulances, etc., but otherwise I don't see why in the world they'd want to ban bikes.
Any chance your doctor at that hospital is cyclist? Or maybe any of the others in the group (if it is a group)? You could always try mentioning this to your doctor. Sometimes the doctors have some pull - many of them serve on hospital committees, etc. They can put some pressure on a narrow-minded CEO.

