NMoasis, nope not true. You need to request that they take care of their trees. Here you can be sued for doing so. If the tree is on their property it's their responsiblity.
It took us 30 years to get our neighbors to take care of their trees out. We had to take them to court, provided them with an arborists letter and every time their trees damaged our fence they would say act of god. We proved that their trees were dangerous and cost us hundreds of dollars. Also check your insurance policies.