My neighbor has hired a tree trimming service to trim their tree that extends over our shared fence. I have never asked them to do so, nor expressed any resentment that it grows over the fence. It doesn't appear to be in danger of falling and causing damage. She has mentioned a few times that I should trim my tree that extends over the fence into her tree, saying that she doesn't want her tree to be diseased from mine. My tree is healthy and not diseased, so I am a bit confused.
From what I have found, I am only required to trim it if it is hazardous or potentially hazardous. Or if the roots are encroaching onto their property and causing damage (fence, septic, foundation). I can't find anything saying that one tree growing into another would spread disease from nothing, though I could just not be looking up the correct thing. I have never had any intention of trimming it, as it doesn't seem necessary.
She flagged me down as I was mowing my front yard to tell me she was paying for trimming my tree, which anything past the property line is perfectly within her rights.
Is there reasonable cause for concern that one tree's branches growing into another trees branches would spread disease if they are both healthy?