Some dogs can and do roam without causing trouble to livestock or gardening. Those I tolerate. Somewhat of a problem is all go through a stage where some trouble is caused and it needs to be stopped quickly. With proper training the trouble making can be stopped and the dog becomes a model member of rural society. Dogs that tend to do best in that regard are not confined as much, do have some sort of purpose involving people (i.e. hunting, herding) and are familiar with all sorts of livestock. Dogs penned up all the time without outlets for energy and mental stimulation tend to be problematic and such dogs can be effectively ruined if owner does not effort to train and excersise them. Dogs are more of an investment than most people realize. They are more than pets. They have smarts as well.
I agre with all this. In a rural area, dogs have a purpose, which is usually to guard and protect livestock, gardens, crops, or some sort of property. It does take training, not just getting a dog and turning it loose. Those dogs cannot do their job if they are penned up. I'm not talking about suburbia. That's different.
Some of my neighbors have dogs that run free and are not a problem. Thye have been trained what is livestock and what is fair game. Occasionally a neighbor gets a pup that needs training. Failing that training can be and usually is fatal, often at the owners hand but sometimes not.
My biggest dog problems are not the neighbors' dogs. People like to drop dogs off out here in the country. I have taken some of those to the pound. It's free to drop them off as long as you are a county resident here. It may be different where you are. I try to do that before they become a problem. But I have also been known to permanently solve the problem using a 12 gauge, #4 shot, Turkey load. Instead of using a shovel, a neighbor suggested I just drag them to a specific place on his property. The coyotes or vultures soon dispose of the carcass.
The problem I forsee your nephew possibly having is that those dogs may have been trained by your actions to leave when they see a human approaching. It may be hard to get a good shot. But if at all possible, they need to be shot on your property. Photos showing damage and them on the property, either before or after are a great idea. Many people in a true rural setting understand how the system has worked for centuries, but some don't. Your nephew needs to protect himself against possible legal claims.
Good luck with it.