The WWCG believes in a type of EENS, applying to them. They are the truth and the only truth, as expressed by armstrong himself. That's interesting.
That's a prerequisite for even beginning to claim that you are a legitimate church, IMO. Scripture is completely clear on that: there is only one Church, and it is a pillar and foundation of truth. When I was in the process of converting, I remember my dad wanted me to join his Baptist church; I asked him "are you guys the one true Church, able to preserve and teach the faith infallibly?", and he gave a similar answer: "there is no one true Church, no one pure and pristine denomination that has all the Truth without error." I basically said, "then you've just disqualified yourself from the running - I'm looking for a church that at least claims to be infallible."
Honestly, if a person says, "no, my denomination isn't infallible," or "no one has all the truth," then why should I listen to anything else they have to say? They've just admitted, basically, that they're in error, or soon will be.