My recollection of what TWI taught is that anybody (including anyone in TWI) that performs Romans 10:9 is born again and is part of the Body of Christ forever. "Incorruptible Seed". Whether you're in fellowship with God or with TWI, or not, you are "heaven bound and no power from hell can stop you from going". And the only proof was SIT and without SIT you couldn't prove or REALLY SAY that you were.
My recollection again: The "Household of God" was interpreted as being "in fellowship" with God and with TWI and in practice with all the principles. It also meant you were an active member in TWI fellowships. Did TWI teach that other christian groups were 'in fellowship with God'. I think that was kinda fuzzy to me. I thought that it depended on whether one was "standing on the Word" and of course the Word was only the TWI version. So yeah, I think the general thought was that TWI was the only "household".