Cherry tree in my yard extends over my fence into neighbor's yard, they want me to hire an arborist to determine the health of the tree (Virginia)

Backstory: A large branch of the tree fell in their yard a few months ago during a storm and they tried arguing that it was my responsibility to hire someone to handle it. I did some research and learned that it was their responsibility since the branch falling was an act of God and not because I was being negligent, so I did nothing and they cleaned up the branch.

Issue: they gave me an legal coded letter basically alleging that lighting struck the tree to cause the branch to fall months ago and asking that I pay for an arborist to evaluate the health of the tree. It doesn't look to me like lightning struck the tree, I think the branch may have fell due to winds. The tree also looks healthy now to my untrained eye (full of green leaves, no dead branches, no signs of rot, etc.) I'm also currently in a tight place financially so I really don't want to spend money for someone to come out to look at a tree that I truly believe is healthy. Is there anyway I can avoid spending money on an arborist or is that the only way to protect myself from the neighbor holding me responsible if another branch falls now that he's alleging the health of the tree is compromised?