The other thing I was wondering is if your neighbor isn't feeding them enough. Some people don't feed much on purppose, to force the chickens to forage more. They end up having to search farther and farther away from the coop, to get enough to eat. Some people also only feed grain, because it's cheap. Then the chickens have to forage really hard, to make up for the missing protein.
It made me think of it again, when I read about the neighbor calling them in. It may be that's when they actually get fed. That would certainly make them come running home. That would also explain their love affair with your yard, coop and feed. If that's the case, you might have a harder time discouraging them.
For new people reading this, I just want to say that my chickens have all been great foragers. They will forage all day long. I've always free fed them. They don't need to be starved on purpose, to get them to forage.