First things first, check the county records to make SURE this is a private road. Most roads (unless it's a private driveway to one individuals house) is a public access easement. If the easement has been dedicated, it's not private and the very dedication grants the 'public' access to the road. His biggest fear here should be criminal damage or trespassing. Every states laws are different but, If he went past a 'private property' 'no trespassing' sign, or entered a closed / locked gate,,, he is in trouble unless the roadway/access easement was dedicated to the public.
By the time this get's to court,,, there won't be any evidence left on the road. Besides, unless he burned into the asphalt and dug holes like novaderrik said,, there was no physical damage. Your uncles argument is everyone wears tires away on the roads so the marks are natural. Unless it's customary for the local authorities to force car crash victims to go out and scrub the skid marks from the highway, I don't think I'd worry about it. My guess is a well worded apology and a promise to never enter the victims property again would bring it to an end. Connected or not, they can't make up new and unusual laws to persecute someone who made a stupid mistake. They will have to find some law that was broken (trespassing, criminal damage etc), and some physical damage to ever get to court.
If it all blew up in your uncles face, a 'fog coat' is the sealer they put on finished paving projects before it's opened to the public. Makes the paving pretty black and looks like new. Because there was no damage to the paving structure, that is the absolute worst he could expect,,, a 'paint job' to hide the normal wear of tires onto what may be a public easement..