You can't prevent people from talking, sad it is in some situations... causing distress you don't need on top of it all...
This is exactly the reason why we don't want lyme forum members going on other Healingwell forums trying to convince people to look into Lyme Disease. (I might even want to use your thread in a possible future discussion - lol).
People tend to be very territorial about a diagnosis, and it is hurtful whenever someone is trying to convince you that your long sought for diagnosis is wrong.
My dr is a cfs/me specialist. He is convinced that these myalgic pains are in fact a symptom of something going wrong in one's body. That is why he tests all of his patients for virusses, bacterial infections, food allergies, leaky gut, etc etc.
You could maybe answer your neighbour that you are happy for her that she has a diagnosis, but that you and your doctor are convinced that Fibro is not what is wrong with you, that your symptoms show otherwise. She probably does this with the best of intentions, but you can't convince someone of having a certain disease if that person is not feeling that.
Trust your gut feeling, don't let anyone make you doubt it.