None of the hens have aged out of laying thanks to the efforts of the local predators. Should that ever happen, it will surely require resolving the question of whether the hens are livestock or pets before I can tell you about how the cooking process varies from a grocery store bird.
Its Wikipedia page: https://en.wikipedia.org/wiki/Paraponera_clavata
Races of chicken that were breed to fight are very slim and all muscle. Not much different than pigeons. Probably a hard meat. Old roosters of most other races are perfectly edible.
Of course locals could have more than one motive to not want foreigners eating the birds. Specially when there is an old and widespread tradition of let the chicken free-range around villages