They are not Ordinaries, however. Therefore, much of what they have done is illicit (wrong), but not invalid. The priests they have ordained are valid priests. The problem is that they have done much that is proper to a Bishop who is also an Ordinary, without being ordinaries.
I recall well the SSPX’s oft-repeated and emphatically-stated insistence in the early days after the consecrations that they did not, under any circumstances, claim any sort of jurisdiction for their bishops. The bishops were there, so the rationale went, merely to provide “traditional” Holy Orders for “traditionally-formed” priests and the “traditional” Sacrament of Confirmation. The SSPX compared themselves to auxiliary bishops.
And in the very beginning, they behaved like auxiliary bishops. They hid their pectoral crosses when appearing in public out of respect for the local ordinary. When they pontificated, they did so from the faldstool and carried their croziers crook-inward in the manner of a bishop without territorial jurisdiction. According to the pre-Vatican II rubrics, only bishops with jurisdiction within their jurisdiction wore the mozzetta; otherwise the mantelletta was worn instead. In observance of that, the SSPX bishops wore the mantelletta, not the mozetta. They observed all of these practices very scrupulously, in fact…for about ten minutes.
It was not long at all, however, before the SSPX bishops utterly abandoned their care to project themselves as non-territorial bishops. The scruple about displaying the pectoral cross in public quickly vanished, the mantellettas were put in mothballs and replaced by the mozzetta, the crook of the crozier was turned forward. By the time I entered St. Thomas Aquinas Seminary in the Fall of 1989 (only one year after the consecrations), Bishop Williamson (the rector) had already abandoned the auxiliary bishop’s faldstool and was pontificating from the throne in the manner of a bishop with jurisdiction (much to the consternation of a handful of concerned MCs and sacristans, apparently).
In time, all of the SSPX bishops began to celebrate pontifical Mass and Vespers from the pontifical throne. With greater abandon, still, they began to erect canopies over their pontifical thrones, and to display their episcopal coats of arms behind their thrones. What’s striking about this practice is that they pontificate in this manner wherever they happen to be in the world, the way that only cardinals may! Even ordinary bishops do not pontificate from the throne outside of their dioceses! But SSPX bishops–in the manner of the Princes of the Church–pontificate from the throne anywhere they happen to find themselves, anywhere in the world.
I have never heard or read an explanation for the SSPX’s change of heart with respect to scrupulously projecting their bishops as non-jurisdictional “auxiliaries”. I have never read or heard a proper justification of the adoption of the liturgical and sartorial attributes of diocesan ordinaries by the SSPX bishops. Ignorance of the rubrics can hardly be cited in the case of the SSPX, particularly when the bishops did, in the very beginning, follow the rubrical prescriptions given for non-jurisdictional bishops when pontificating.
When I was at the seminary, I did enquire of one of those few concerned MCs what Bishop Williamson’s justification was for presiding from the pontifical throne as opposed to the faldstool. The MC I spoke to responded, “some nonsense about not wanting to confuse the faithful, who aren’t familiar with the rubrics of pontifical Mass at the faldstool.” As if the faithful in 1989 were familiar with the rubrics of pontifical Mass at the throne!
The fact that SSPX bishops pontificate from the throne may be the Church’s least concern with respect to a group of previously-excommunicated renegade prelates suspended by Rome with no faculties or jurisdiction; prelates who pretend to shepherd and even govern the faithful adherents of an international organization that denies the Holocaust, that has given refuge to Nazi-sympathizers, and which allies itself with the extreme-right political fringe, with the monarchist-restoration movement of France, with the notorious TFP, and with any number of reactionary movements.
But what does this usurpation of the liturgical prerogatives of diocesan ordinary bishops–and even of cardinals–say about how the SSPX bishops actually view themselves?
Here are some links offering images or videos of the SSPX bishops officiating from the pontifical throne in the manner of jurisdictional prelates:
Richard Williamson (images):
sspx.org/RCRpdfs/2009_rcrs/march_2009_rcr.pdf
Bernard Tissier de Mallerais (images):
google.com/imgres?imgurl=http://www.laportelatine.org/district/chartres/lourdes2009/report/tissier001.jpg&imgrefurl=http://rorate-caeli.blogspot.com/2009/10/we-present-here-first-photos-of.html&usg=__I2QBDPDPX5HQwofsX7iVzRWzt7U=&h=488&w=650&sz=98&hl=en&start=1&zoom=1&um=1&itbs=1&tbnid=K9qFCZPNntaiyM:&tbnh=103&tbnw=137&prev=/images%3Fq%3Dsociety%2Bof%2Bst.%2Bpius%2Bx%2Bbishops%2Bpontifical%2Bmass%2Bthrone%26um%3D1%26hl%3Den%26sa%3DN%26tbs%3Disch:1
Bernard Fellay (images):
sspx.org/RCRpdfs/2009_rcrs/july_2009_rcr.pdf
Bernard Fellay (video):
laportelatine.org/communication/videotheque/MgrFellay100110/10janvier2010.php
Alfonso de Galarreta (image):
google.com/imgres?imgurl=http://cache.daylife.com/imageserve/09BY5fN92bc6o/610x.jpg&imgrefurl=http://www.daylife.com/photo/09BY5fN92bc6o&usg=__lfw_azIm3eIYUg_e3uLgXI-ugpI=&h=406&w=610&sz=80&hl=en&start=9&zoom=0&um=1&itbs=1&tbnid=oVL7Gij28uuBRM:&tbnh=91&tbnw=136&prev=/images%3Fq%3Dbishop%2Bde%2Bgalarreta%26um%3D1%26hl%3Den%26sa%3DG%26tbs%3Disch:1