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.