Maybe but maybe that limb served a irreplacenable function.. As others noted the tree has had some large low stuff removed, but who knows? Maybe that limb blocked the neighbors motion light?
Possible, although that was not brought to our attention. However yes in that case a tree planted to grow up and cover the light would not be unreasonable. However not taking the rest of the tree down.
There is one other possibility here and it is that the neighbor told the tree contractor, "go right ahead I have their permission for you to drive in and do the job."
"But there is also a branch in the way we would need to cut."
"Don't worry about it I already asked them and they said no problem."
People lie all the time about permission and access.
It is usually easy to spot though. The minor details. A "they won't mind" means nobody ever asked and the person is assuming and will throw you under the bus afterwards.
I just called a woman and her husband out on that the other week.
A vacant property next to her where I was asked to park in the driveway, cut three trees back to the trunk. All belonging to the other property. They gave me a bunch of b.s. explanations I didn't care to hear. Including that the city even said to go right ahead. They probably said she can cut whatever hangs over her property. The place is kept up.
I simply told her it would be trespassing for me to go over there without permission from the owner or custodian of the property. Any made believe additional cracks in the old driveway would be seen as my responsibility to replace the driveway. The trees which would eventually die would have been my responsibility to remove and replace as well.
It was at this point I was informed she had received several other estimates and that mine was the highest to prune only what was over her yard and she would have to go with someone else.
No doubt all non Arborists conducting illegal pruning. I said well good luck and left.