Here is some interesting reading about thunderstorm fears being linked to separation anxiety issues. Fear of Thunderstorms and Noise Phobias
I don't think I would try these technquies with a dog that I am not familar with. You may show this to your vet and see what he/she thinks about this article. It may be something that could be considered once your dog is comfortable with you. I think the most important part was that your dog should not be petted while showing fear.Because it is being rewarded for fear behavior. I personally would have petted my dog thinking that I was comforting it. As for the greenies, I have never given them to my dogs, but I did see they were recalled from petsmart a few months back, not sure why. Good luck with your dog, she is lucky to have a new family that is willing to work through her problems.