I think it's more complicated than that. Take a closer look at the map shown in the article:
Scroll down to near the bottom, in the center laterally. There's a note box that reads, "A gate restricted public access to a section of Boise Ridge Road that cuts through Wilks property." That's a real road, on a map, not some logging trail. It leads from public land to public land. If it isn't illegal to shut down access to public land, it should be. Notice a bit to the right of that gate there's another tract of Wilks land, that has state route 21 running through it. If Wilks has the right to block Boise Ridge Road, then they also have the right to shut down state route 21. Is that what anyone (other than maybe the Wilks brothers) wants?
Also notice just to the right of the circle pinpointing where the gate was erected, there's a small rectangle of public land that's completely surrounded by Wilks land. I don't know about Idaho, but in this state it's not legal to landlock a parcel. If that smaller rectangle is public land, it would seem that the Wilks should have to provide/allow access to it.
North of the gate on Boise Ridge Road, about in the center of the map, there's a location where state route 55 runs through a tract of Wilks land. same question: If they have the right to block Boise Ridge Road, then they also have the right to shut down state route 55. Maybe they have a right to erect a toll station. Do we want that?
Again, I know nothing about Idaho law. Where I grew up, in Connecticut, if land was open to the public and used freely by the public for a period of time (I think it was fifteen years), the land owners and their successors lost the right to prohibit public access in the future. That's why when buildings were built on street corners and the building itself was set back or maybe angled, creating a small plaza between the sidewalk line and the actual building, the property owner would embed a small bronze plaque at the actual property corner reading "This space not dedicated," meaning that the plaza beyond that marker was not public space, so in the future if they wanted to build a building that came right to the property line, they could. The public couldn't claim they had a right to use that space in perpetuity.