Yes, private property. But were the spaces "legally enforceable"? There would be a citation to the law on the sign. The analogy is 15 min. parking at the mall. Without reference to a legal citation on the sign, it is a 'request', rather than something you would pay a fine for, as you would for improperly using a handicapped parking space.
My point is anybody can post any inane sign on private property. My concern would be if such parking spaces were sanctioned by law. I doubt the signs you and K2 saw are.
AK