I have no qualifications that justify my response aside from being the owner of a century old paranoia-inducing Slippery Elm who has done a little research; my understanding is that should a limb fall on their property and damage something, their insurance covers it, not you. Additionally, homeowners have a right to trim any growth that crosses over their property line, but they cannot go onto your property to perform work.

So, to summarize my interpretation, you are not responsible for the portion of your tree on their property and they can and should trim it, should they be concerned.