HURT on SOMEONE ELSE's PROPERTY- Who's at Fault?

I believe the most persistent Legal Myth is that if you are hurt on someone's property that the landowner is "Automatically Liable."

That is NOT TRUE. 

It has never been true anywhere.

But, I do think I understand where it came from. If you are at my home, and you trip over your own two feet and break your leg, I am not liable. In other words, nothing I did--or did not do--caused you to fall. But, I have medical payments coverage on my homeowners that may pay medical bills regardless of fault.

So then, your mother hears that her son fell on my property and all his medical bills were paid. Her conclusion is that I was liable, so my homeowners paid. The Myth grows.

But, Homeowners would not, in my example, pay things like pain and suffering, lost wages, etc. Only medical bills would be paid and only to the limit of coverage (usually $5,000.00). 

Another problem arises when the homeowner is clearly at fault, but it was NOT an accident.  Such as if you get into a scuffle during a ball game in the homeowner's yard. If the homeowner breaks your jaw with a punch, that is an intentional act, not an accident. Therefore, homeowners will deny the claim. However, again, they may pay medical bills under medical payments coverage.

Finally, though, lets say that the homeowner left a hole in the dark flower bed and you don't see it and your ankle is broken. That would be an accident, caused by the homeowner and likely covered.  The negligent act was leaving an open hole that was not obvious and created a trap of sorts for visitors.

This is not the only Legal Myth out there, but it seems to be the most pervasive. 

What do you think?