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It Depends(tm).

Practically you’re right of course, but they are probably technically responsible given the circumstances the poster laid out.

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A landowner is definitely not "technically responsible" for cleaning up trees that fall along or across the border of their property.
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If they are aware of a dangerous situation (diseased trees), and don’t do something about it, they are definitely on the hook for property damage caused by that negligence.

It would boil down to their degree of plausible deniability, ‘state priviledge’, and the specifics of the law and precedent in their state of course.

Good luck

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The situation described says nothing about diseased trees. It says "I live next to a forest and trees fall."
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