Not an American, but I really don't get these stories. It has to be legal to enter somebody's driveway, right? How else are you supposed to ring someone's doorbell?
It absolutely is and the people who shoot at others for showing up on their property are 100% paranoid assholes watching too much Fox News. Hell, you can even legally camp on private property as long as you're not within view of the house. I don't suggest doing that, on account of the crazies.
Wait a minute tell me about this law that says Americans are allowed to camp on private property: like they can do that without permission of the property owner? as long as not within view of the house?
Many EU countries have freedom to roam laws to allow access accross undeveloped private property, this includes as you said camping as long as you leave the land as found.
In the US i know of no state allowing such, and the ability of the person traversing the land to sue the owner means the default is no treasspassing signs everywhere. this isnt to say if you were unsure if the land was private and there is no sign/indicator of tresspassing you coulding walk through but that isnt strictly giving you the right to access the land
in western States quite a bit of land is federally owned and behaves more like right to roam, this has made odd cases there is a cheker board patern between two federal land areas and private property and what to do when a hunter says steps over the corner of the private properties between the two public access areas.