I have never heard anyone state this absolute fact, which is so very obvious.
The situation stands exactly like this: The Holy Roman Catholic Church, headed by the Pope in Rome, His Holiness Pope Benedict XVI, has presented a docuмent to the Pius X Society stating exactly what must be believed, unequivocally, ie. given full assent of the will, in order to be a member of the Holy Roman Catholic Church. They were given the non-negotiables.There's no hedging. There's no arguing. There's no equivocating. There is only "yes" or "no." That's it. And there's no going back.
If the Pius X Society refuses to sign, they clearly have moved outside of the Church and can not make any sort of claim to the contrary.
If they do not sign, they have undeniably broken with Rome, they are formally in schism, and are unlikely to ever return to communion with Rome again.
I may not be correct on this, but I do believe that most of the Pius X Society would abandon the Society and return to the Church of Rome under these conditions.
I believe that Archbishop Lefebvre would sign under these conditions.
If you deny even one article of the non-negotiables, that's it, you're out and so is your soul.
Essentially, the Pius X Society does NOT HAVE A CHOICE. If they want to continue to claim that they are the true Catholic Church, and continue to consider themselves Catholic, they MUST sign.