Only highway vehicles (as defined by your states Code) can get you in trouble for running off-road fuel on the road..
In some states even vehicles without a current registration/tags (ie have the hand written 'farm use' plate) are still considered 'highway' vehicles - it all depends on your states laws..
NC also dips tanks. They got a guy earlier in the year at some event near Charlotte NC. He was running Bio Diesel. He had stickers on the car advertising the fact and said so to the officer. He had not paid the tax. The Farm Show I go to is at the NC Fair Grounds. Pretty sure that is state property but I have not seen or heard of HP dipping tanks during the show though I bet they would get some violations. I have heard of them dipping at NASCAR events.
In NC an area that is on private property but used by the public has its own unique status, its called a PVA, Public Vehicular Area. If you have an accident in the parking lot of a grocery store it would be marked on the accident report as happening on a PVA. Not private property.
We have a gate across the road at the point were we own both sides of said road. From the gate it private property. My kids could drive the car if they could reach the controls no license needed. I would not have to register the vehicle if it was never went past the gate. But if said vehicle went past the gate to pick up the mail it would have to be registered since at that point it is on a PVA. And the kids would have to had a license to drive past the gate. From the gate to the paved county/state maintained road its a PVA not a public road. If the HP wanted to dip my tank on the PVA they could I supose. Not sure what reasonable suspicion or propable cause they need but it is a PVA not private property. Past they can't do a thing. Its irrelevent if I use taxed or untaxed fuel.