Going by plain logic I would say it is a complete myth, I mean why only local honey? It is a great excuse to stock up on every honey from every county though, just to be completely immune
Theory behind local honey being that local bee's are gathering pollen from the very flowers and tree's in your area that are producing the pollen you are allergic too. So if their honey contains these specific known allergic types of pollen then it might help you form an immunity through introducing small amounts of that pollen by eating the honey.
So that's the theory, but I don't think it works. I have local honey from a bee keeper who stays one street over. Whilst it is utterly amazing and the best honey I have ever tasted in my life, it's doing naff all for my hayfever.... She said I need to take it all year consistently and if it works I should have built an immunity by next hayfever season..... But then, I bet she just wants me to buy a jar of her honey every 2 weeks, eh?
At this point in time I am willing to do ANYTHING to get rid of hayfever.