Bishops do not like mere priests taking the initiative; there is a chain of command. Bp. Tissier came down hard on these priests for not obeying their "generals". And Bp. Williamson would not openly back them unless it was his idea.
Come on Wessex, that last sentence is too cheap. :-) You know he's a very humble man. The bishop was and is in close contact with the resistance groups, including the one of Fathers Joseph Pfeiffer and Chazal. And so the bishop advices the resistance priests in a certain way. We can see it when we listen to the sermons of Fathers Chazal and Pfeiffer: both are inspired a lot by Bishop Williamson, also with current ideas (one time Fr. Pfeiffer preached by reading aloud an EC).
Usually the bishop has excellent reasons to do or not to do a certain thing at a certain point in time. Many times we only learn later why this was the case, because he does whatever providence indicates. So, Wessex, let's not forget providence! Because Bishop Williamson is on Our Lord's side.
His trip to Brazil was to serve an existing independent group, although I think he was testing the water to see how SSPX officials would respond. He may not repeat such a move. He is a survivor and will measure accurately the amount of leeway his standing and adversaries afford him. This could go on for years.
It will hardly go on for years.
For one thing Europe and probably other parts of the world will likely be on fire in one year or even earlier (well, the border between Syria and Turkey is already on grenade fire right now and the NATO will have to act). And concerning the doom of the Euro and its resulting (civil?) wars, just listen to this bright Scotsman Nigel Farange.
But for another thing Bishop Fellay really wants to get rid of Bishop Williamson for a long time now (and on Rome's side it could even be a pre-condition for any re-union. That's a speculation, but a reasonable speculation I think). So the expulsion of Bishop Williamson from the SSPX doesn't seem so far away. He formally received his "canonical warning" already some month ago, or so we've been told from some good sources.
How much reaction would there be if Bishop Williamson was thrown out? One might well fear, not much, but that is in God's hands. If he was thrown out, what would he do? I think it's safe to suppose that he would answer invitations from wherever they come.