200' away, this neighbor is? (Sound like Yoda, do I not?) Are you sure that is the distance? That sounds like a more rural setting than a "city" setting. Noise travels, what ever the distance. 21 hens may have a valid point. Perhaps this neighbor is bored, and may be the type of neighbor who's not happy unless she has something to be unhappy about.
Just b/c you don't see any tracks, that does not mean the birds don't perceive a threat. My roo gives the warning call when a truck goes up the hill behind my house... well over 200' away, and through the woods. Airplanes also will set off the warning call, as do blue jays and crows. An owl could be on the prowl, or even a neighbor walking down the street. A mouse or rat in the coop or run could be cause for alarm.
Chickens are loud. Some more so than others. Can you put a hedge around your coop/run? That will help block the noise.