“Traditionalist Catholic” thinking is all over the boards. Those groups such as the FSSP and ICKSP, which have the full blessing of the Church, affirm both OF and EF as equally valid, and all post-Vatican II sacraments in the new rites as being valid. Then there is the SSPX, other independent groups that acknowledge Francis (or at least Benedict) as Pope, and “sedevacantists” who say the Holy See is vacant. It goes all the way to “ecclesiaprivationists”, who say that the post-Vatican II church has ceased to be the Catholic Church, and that none of its bishops, priests, sacraments, or Masses are valid, and “conclavists” who have attempted to elect their own popes (these tend to be very, very small groups). It’s a broad spectrum and there is some overlap.I get what you are saying, but I was going straight on the “valid” wording. Since valid means the bread and wine actually become the Body and Blood of Christ. There are people that claim to be Catholic, however you will find them claiming that only the TLM can be valid and Ordinary Form Masses do not, for the lack of a better term, have the ability for transubstantiation, thus the “novus ordo” is an invalid Mass across the board. Since the OP’s friend attends a parish staffed by the FSSP, I would highly doubt he’d find this idea there among the fellow parishioners, however, should he decide to take more steps further into the Traditionalist Catholic movement…who knows what he may find people believing and trying to pass off as official Church teaching.
My own stance is with the FSSP and other groups (including diocesan priests) who act subject to the local bishops, with much sympathy for, and substantial (not total) agreement with the SSPX as well. As far as the other groups, I understand why they do what they do, why they think as they do, I do not condemn them as “bad Catholics” or as formally schismatic, but I don’t agree with them.