If the bees are in a man made hive they need you to remove honey so that they have room to lay. If you don't they will leave and not all of that honey is going with them.
Honeybees produce more honey than they need for several reasons, mainly that a) they are natural hoarders, b) we've bred them to hoard even more.
It's true that colonies can become pollen-bound and/or nectar-/honey-bound, and thus have too little space for brood. When this happens it's very likely that the colony will swarm off, leaving behind as few as 20% or so of the bees behind, as well as and swarm cells from which one victorious queen will emerge, and then the rump colony will have plenty of honey while it's weak and recovering its numbers. During that time they'll consume whatever it was they had too much of and thus make room for brood.
Yes, and you will have happy neighbors... I do understand that the natural reproduction cycle isn't quite that simple. However for "normal" operation some removal is beneficial and not "stealing", so long as they have adequate supplies.
Not only that, but what beekeepers do is give the colony more room as it fills the hive with honey. The bees don't realize they have enough and just gather more and more, thus ending up with a large surplus that the beekeeper is happy to harvest.
The neighbour example is about wild critters getting the harvest from your own yard vs. your neighbour running a farming operation and keeping the proceeds.
