Starting off, Plant in question is a Cordyline, rather than a palm..
With that said, the two types of plants behave similarly in that the roots of both aren't generally considered a danger to foundations / other nearby concrete or asphalt surfaces since they aren't as woody as roots produced by trees ..Plane tree, Elm, Oak ..those sorts of things for example..
That said, ..from the angle of the pictures, it does look like it is planted a touch close to the house ..which might not allow enough room for the trunk to expand ..which could cause issues later. Then again, these ..and look - alike plants in the Genus Draceana, are planted all over the place in California, within 10ft of a houses foundation and i've never heard of anyone having damage - related issues as the bases grew larger. ..Not to say that can't happen though..
As for any concern involving the roof, A: I'd have whomever did the survey prove the branch closest to the roof is causing damage to it ..And i mean proof beyond any sort of refute..
B: You could trim off all leaves below the roof line ..so that the canopy stands above it ( Leaves can't " mess with any drainage from the roof if no leaves are blocking the flow of runoff off that specific area )
If any branches growing near the roof aren't rubbin' against it, then there is no issue ( ..caused by them )
If you are actually forced to remove it, branches of these are very easy to re-root, so, ..while you might end up loosing the original plant, you could stick any branches you save in the ground a little further out from the roof ...Say near where the fences meet, ..what looks to be the far right corner of your pictures.
Yea, that might block the view of ..what looks like some sort of Barberry ( Berberis / Mahonia sp. ) a bit but, ..at least you'll still have the plant.
As for your neighbor? ..As long as any branches aren't hangin' over their side of a shared fence / wall, they have no say in what you can grow ...on your own property.
Sounds like you've gone beyond being a respectful neighbor in doing your part to keep the plant out of their way.
Shot in the dark guess but, if they whined about any leaves falling off your plant that would end up in their yard, I'd bet they were the type of people who complained about any / everything any chance they got. Don't doubt you're glad they're gone.
I'd throw a party to celebrate, lol.. Good luck.