I know nothing of the sort and if I were you I would not presume to judge the intentions of the two authors of this letter.
I also find it interesting that although there is nothing in this letter in regard to SSPX, or Bishops Fellay and Williamson, people including yourself cannot help themselves but to bring to bring it up. I once stated that instead of trying to answer traditional Catholic arguments, concilliar Catholics just try to shut down the discussion by making sweeping accusations against traditional Catholics and inciting flame wars, a statement to which you vehemently disagreed. If this is not true, why don't you post any specific objections you have to what is said in this letter instead of bringing up the SSPX, which is not the subject and which will surely incite anger amongst the readers and end any fruitful discussion.
"In saying this, we know that we are doing nothing less than publicly reproving the Vicar of Christ".
There's your show-stopper.
I'd say the show-stopper is in the claim that one must be one or the other, but can't be both. Since, presumably, traditional Catholicism (as defined by you) is authentic, the inevitable conclusion is that by your lights, "conciliar" Catholics are not.
So the question arises: if a conciliar Catholic presented himself for Holy Communion at a trad chapel, would he be allowed to receive? If yes, WHY?