A random search turned up this article. It turns out that when a business in a strip mall (like the Rice Village) posts a sign saying that only its patrons can park there and others will be towed, it doesn't have the force of law unless it meets certain requirements. "It has to be the red and white sign with the universal tow symbol saying unauthorized vehicles will be towed away."
A story of a woman challenging her towing in tow court gives the money quote:
"I think it's great," she said. "I did not need a lawyer. I did not need anyone by my side. I had God by my side and I did it."
I know I've been intimidated by these signs. And honestly, I still am, because even if it's not a legal tow, it's still a pain to have to go to court.