I am guessing since the source of damage is "environmental" and not a direct from the player. Otherwise, from a coding perspective, you'd run the risk of angering the horde of cuckoos if you light any part of the environment on fire, even inadvertently, and a dumb bird walks into it. Would also probably require tracking the origin of an environmental fire, which could be the player, or a lightning strike, or a fire blob, or some other enemy that uses fire weapons, and I'm not sure the game bothers tracking all that.

Could also just be a direct interaction with fire to turn the cuckoo into a cooked whole bird with no angry flock no matter what. Not sure if the same happens when shooting them with a fire arrow or hitting with a fire-imbued weapon or anything like that, but I'm happy to (let someone else) try it out and report back with findings.