This quote misunderstands the zombie thought experiment as used by Chalmers. Chalmers actually thinks zombies are impossible given the laws that actually govern the universe, and possible only in the sense it's possible the universe could have had different laws (or so many people would claim.)

I'm not as sure about Putnam's views, but I suspect he would make an analogous claim, that his thought experiment only requires Twin Earth to be possible in a very broad sense of possibility.