Jesus, OK. So liability is specific to "many places and circumstances..." Also Define "relatively few situations"
Fact is, owners CAN be held liable, if they get taken to court--which is why some states and locations require specific forms of insurance to cover this crap. We all know that even if owners try to protect themselves and they' re technically not liable, people try and sue them for stuff. I'd wager the vast majority of property owners don't want you on their property without their permission
http://wiki.legalexaminer.com/help-center/articles/legal-issues-and-property-owners-liability.aspx
How about this: probably 99 times out of a 100 times, if a trespasser you weren't expecting to trespass on your land injures himself on your property and sues you, if you have the guts to take it to trial, you will win. The laws vary from state to state - in some places, the trespasser is always just SOL, in some places, not many, the trespasser has almost the same rights as an invited guest, but for the most part, and in most places, unless you did something deliberate to harm trespassers (like a spring gun or a concealed excavation), or unless the trespassers were kids and you put an "attractive nuisance" on your property (i.e., something other than an interesting piece of yamadori), you'll have very very limited duties to protect from, or even warn the trespasser about, dangerous conditions on your property, much less make sure that they don't do something stupid and harm themselves. Absent such a duty, you have no liability if someone trespasses on your land and breaks their neck or gets eaten by your dog, or whatever.
The link you cited talks about premises liability to invitees. These are the majority of premises liability cases, and they involve people who have the right to come onto the property in places like stores, churches, restaurants, government land and the myriad of other places that you can walk onto without being a trespasser. But there are totally different circumstances when you are talking about people who aren't allowed to be there.
Here's a somewhat better link, which addresses liability to trespassers.
https://premisesliability.uslegal.com/duty-owed-trespassers/
Frankly, not as good as some of the material I used to hand out at MCLE courses, when I was lecturing other lawyers about defending premises liability tort claims, but it gives a decent summary of what the deal is.
So what kind of claims could be brought? Here are some example: You plant land mines around your marijuana farm, or load a spring gun to shoot and kill anyone who enters your cabin in the woods, you leave open mine shaft tunnels adjacent to a popular hiking trail, you keep a wild chimp on your property and sometimes forget to lock his cage, even though you know the high school kids often use your back yard as a shortcut to the practice field. There are all sorts of odd situations in which a court might find liability, but those odd cases are rare, and easily 99% of the time, if a trespasser gets hurt, even because you left your property in a dangerous condition, you, the landowner, will win.
tl;dr: The idea that trespassers who get hurt while trespassing can usually get loads of money by suing the landowner is a myth. It rarely happens, and only under very limited circumstances.