I have no problem culling chickens. I have had to cull a nice showgirl I was very pleased with, not pleasant. If I were keeping the bird as a pet and not a potential breeder it would have been a different story, consulting with a vet would have been in the cards.
Some avian vets only see exotic birds, not 'barnyard' fowl. This is a pet to her, she is within her right to seek veterinary attention for her pet. The same argument, pet versus livestock, occurs frequently within the equine industry. It is a personal choice as to how much an individual vales the function of the animal (riding, laying eggs) over the value of a non-functional (in the 'traditional' sense) existence.
We value our dogs and cats as pets, and as such there are regulations in place to prevent mistreatment. Additionally, social pressures would urge a person to seek veterinary attention for a dog or cat suffering from illness- but in some countries dogs and or cats are also eaten. The difference is simply the value the individual places on the animal- with the value society places on the animal as a secondary influence.
I am not condoning eating dogs or cats, but I am supporting her decision to seek treatment for this hen based on her value as a companion animal for the OP's family. We cannot compare this 'pet' to any old barnyard hen- to them she is more and that cannot be disputed by others. It is based upon their relationship with the animal in question.
Personally knowing that email systems sometimes are set up with spam filters and a person that is a member here is likely to have this forum on a domain is good list, I'd PM that party you first mentioned. That way they'd get both an email notice and a notification when they get on the forum to read posts etc....