Getting rid of tree roots in very tight parameters

[Amir Navabpour]

I have a tall tree (so probably deep roots), that is about 1 yard from the side of my house, and the neighbors fence less than a foot behind it. The tree guy said he can cut it to a stump without taking down the fence, but to grind the stump would need to remove the fence which I want to try to avoid. Here’s my question, I read that you can cut a tree down to the stump and then paint herbicide on the stump and that should kill the roots. My general contractor said that approach isn’t a guarantee to work. As it depends on how deep the roots are. Being so close to the house I want to take care of asap to avoid damage to the foundation. The needle I’m trying to thread is getting the roots addressed without having to remove the neighbors fence that is a foot behind the tree

Anyone have any suggestions on how best to address this?