If a car is parked on a private lot with a towing warning, can only the tow company listed tow vehicles from the lot?

Question

And would the tow truck company know if the lot owner was legitimately calling for a tow?  

Answer 1

You are only supposed to call the tow companies on the list.  The tow truck does not know if the call was legit if the car has no park stickers.  But prepare to get SUED left and right (and be charged by the police) if you called for a tow on a car that is legally parked.

Answer 2

The owner can call any tow company he wants. Do not park there and you will not have any problem worrying about this.