That is correct. Those two limbs are the ones he is wanting to remove.
After talking with him again a couple of days ago it appears this is a project he wants to undertake this fall. He is in the process of roofing his house and by the sounds of it won't be able to financially commit to the limb removal until then.
He asked if we had made a decision about letting him have access and I told him we haven't decided yet.
I had a tree growing over my roof like that, and I wanted limbs removed before I got a new roof, as it kept dropping limbs on the roof. Never any damage, but I didn't want to risk a NEW roof getting damaged, and being an oak, it also stained the roof horribly. It's actually the neighbors tree, or I would have cut the whole thing down as it's slowly dying and drops acorns by the thousands every fall. They were not agreeable to that even though I was paying for it, so I removed everything that ran over the property line. It was/is growing much worse over their roof, and is dropping huge limbs on it, and when it goes completely, it will be on their house. Never could figure out why they wouldn't let me take care of the issue for them.
They climbed the tree and lowered the pieces down to another couple guys standing on the roof. Normally I would not want a bunch of people walking all over my shingles half the day, but like your neighbor, I was getting a new roof anyways. So there is a way without using your property.
Even with a bucket truck, limbs like that are going to need to be cut off a little at a time, and lowered down.
If you do let them do it, make sure they are not driving over a drainfield or anything like that. They can cause damage that won't show up for a couple of years. But I would say NO.