That doesn't make you inherently responsible for the tree falling down in a freak storm 3 decades down the line.
We can't find someone to blame for forces of nature. This includes an earthquake, tsunami, etc. Insurance can help recover from these events, but nobody is "responsible" for the events happening. This may or may not include healthy trees falling. LLMs are not a force of nature, and we can and do expect them to have erroneous output. We can and do assign responsibility to the humans who use LLMs. Again, they are not a force of nature. We control them, we give them the ability to do bad things, so it's pretty obvious that there would be responsibility and blame attached for when things go wrong.
Modern AI has more in common with an ocean wave than it does with a hammer or a gun. It does its own things. It doesn't care. It will fuck up someone's day.
Best one can hope for is that the right lessons will be learned when that happens. Which, of course, hangs on there being anyone to learn them afterwards. Because the scope of "AI oopsies" will only ever increase.