I'm surprised that you were not aware, but come to think of it, I just realized that there's still that myth of illegitimacy or "non-canonical" status floating around among trad groups and N.O. alike.
Define "illegitimate" and "non-canonical". As far as I know, it's no myth.
Legitimacy: The SSPX's argument still makes little sense. In 1970 the SSPX was canonically established, and received
temporary permission from the Church to operate as a
pia unio for 6 years, presumably as part of the process to becoming a religious order. Then in 1975 the SSPX was still on that same trajectory, but was unjustly (and perhaps illegally) suppressed. Granting both of these claims, how does it follow that the SSPX
is (today) a full-fledged religious order? Unless and until they receive this status from the Church, they don't have this status. It doesn't matter that they were on the trajectory... they nevertheless have not (yet) received it. And while Francis may have given them many allowances, not even Francis has given them the status of being a full-fledged and autonomous religious order. Again, their argument makes little sense. What they're basically saying is not only that the 6-year period was stretched indefinitely into the future (which, at least in my opinion as a non-lawyer, sounds pretty absurd), but also that they somehow acquired a status above the status that they had back in 1975 (in 1975 the SSPX was a mere
pia unio, and not even a permanent one. Now the SSPX claims itself to be a full-fledged religious order, and has proceeded to set up its own chapels and its own hierarchy).
Canonicity: Even Bishop Fellay (in the article that user St.Justin quoted) admits that the SSPX is "irregular". If everything was perfectly fine and legal, then why would Bishop Fellay acknowledge the SSPX to be "irregular"? Why wouldn't he insist that the SSPX is
not at all irregular, and further assert that the conciliar hierarchy is wrong for failing to acknowledge this simple fact? Seems that the SSPX, or at least Bishop Fellay, believes that the SSPX does not have the same legal status as e.g. the FSSP.