Re: Damage to Plants on "My" Side of the Neighbors' Fence
No, they do not have the right to come onto your property to do anything without your permission. So, when you can prove who did come onto your property, you call the police and report the trespass.
in the same vein though: you have no right to allow your plants to grow onto his fence. Especially if this is a wooden fence, vines can cause considerable damage to the fence. Would you want the neighbors plants damaging your fence?
I am not an attorney and any advice is not to be construed as legal advice. You might even want to ignore my advice. Actually, there are plenty of real attorneys that you might want to ignore as well.