That's part of the problem in the US. Hunter tripped on a branch? That's a lawsuit!
However, "attractive nuisance" has gone pretty far, at least here in California.
edit: I think the parent commenter edited their comment, but I'll leave mine as-is.
If it can happen when a thief breaks into your house and breaks his leg.. it can happen in the woods.
Of course: depending on state, etc.
People who live in rural and semi-rural areas in the US are mostly pretty chill in general with people respectfully using their property, especially at the edges, in my experience.
This is a non-sequetor and is most cettainly false.
A house is hypothetically meant to be safe, woods are not - you could be eaten by a bear.