The WTS's argument is that any changes to the Bible did not change the meaning of the texts, and so the message remains as it always was. That certainly would not apply if the name of god had been removed from all of the NT texts. If your mission is to establish the worship of the true god, and that god's name has been wiped from the sacred texts you use to make your case... you cannot make your case.
I mean, if the devil can make it so the name of god is removed from his own letters to mankind, then what changes and alterations are beyond his ability?