I own a towing business. We do not do private property tows or any tows that are not authorized by the owner of the vehicle unless the police call us to impound the vehicle and keep it at their lot. Too much abuse.
The towing of vehicles from private business's parking lot has been a big issue locally but has met with some resolution.
There must be signs that have to be of a certain size, height and distance from each other. The warning must state clearly the parking restriction, cost and payment method, name of towing company and, phone number to claim vehicle.
The point was to recognize both the vehicle owners AND property owners rights.
I know many of these towing operators and while I don't socialize with them I have never seen them sleep upside down or drink blood, target NSX's or any other car in particular.
Like any group of people there are some that are just plain mean or stupid but it is not the rule but the exception. The vast majority pay their bills being service oriented, are good dealing with the public and often provide emergency services that they never get paid for because the customer just wasn't expecting the need for the service and had no money. Sometimes they even save lives.
As for the subject of unauthorized tows, the tow operators can be the subject of verbal and sometimes physical abuse by people who are clearly arrogant and indifferent to the rights of others and are only been towed or booted because they want to save a few steps or not pay a parking fee.
The owners of business's near bars that let folks park in their lots are rewarded with, broken bottles, used condoms, trash, vomit, emptied ash trays and urine that the next morning their customers must tip toe through until they get out to clean it up.
(I hope you don't drink and drive your NSX)
Chances are there are towing regulations in your town too. If the standards required by the property owner have not been met you may have a right to restitution and should persue it.
I wouldn't think of parking my NSX or any of my vehicles where it may be towed and would be glad to walk the extra distance or pay the fee for legal, secure parking. I don't want to pay a tow operator either.