Noooooo! How awful for you! We have one (1) roo and he's vociferous, but to date have had no complaints. That's probably because in the dead of winter everyone has their house locked up tight and fly South.
Fortunately, there is only one neighbor in this small community who complains about anything (and everything). She's the one with the yapping auxiliary-back-up dog. Go figure.
I agree that they should have approached you first with their concerns instead of calling animal control. Not everyone is especially kind.
I'd rather hear roosters crowing, dogs barking, cats meowing, woodpeckers pecking, birds talking, crickets chirping, and every other sound of nature instead of enduring these freaking jet water skis and boat motors. Oh well, can't have every thing you want, eh?