I am going to play a little devils advocate here. as I can kinda see the parks point....and from a liability standpoint. Without the car tag, then tow truck driver is not a guest of the park... and most likely would not be covered by any general liability policy covering park guests....for damage suffered or caused by same tow truck driver doing whatever he may do.
You then would think that the tow trucks insurance would kick in to handle damages suffered or caused by the driver while in the park, but here again this could be tricky, and may be why the park would require pre-authorization for commercial business conducted on their property. A prudent property manager would verify the commercial business had insurance and would cover any damages suffered or caused by same........ since the propertys liability insurance most likely has a disclaimer against commercial business activities on site.
It's really not a whole lot different than you having a party at your house, and one of your guests decides to change his oil in your driveway. He hires a mobile oil change guy, who then accidently spills the oil which contaminates your yard and then it also runs down into the storm drain contaminating the water. You allowed the guest on your property, but not necessarily the oil change guy, who you just found out forgot to pay his last months insurance and it got canceled. Now they are all kind of fines, as well as damage to your yard. Your homeowners insurance company won't pay, as they say their policy doesn't cover commercial businesses on your property. See the mess that can be just beginning here.
Many people here, may have also never been involved with what happens when a roofer you hire, hurts himself on your roof, then you find out his boss didn't have workers comp. This guy can come back on you, and many many court cases have went against the homeowner...who is liable for all lawful activity on his property.
The parks are no different, and are liable for all lawful activity occurring on their property. if they determine that they need to approve all commercial business done on their property, or even require that all guest are properly tagged with their vehicle...so that they are covered insurance wise...then I wouldn't really get upset. I would actually expect such.
You can now throw all the rocks you feel at me.