Independent Catholicism (another way to refer to the "valid-but-canonically-independent" phenomenon) is an interesting creature in the world of Roman Catholicism.  It traces its validity to the early Church, and a controversy that raged very early on.  The controversy centered around the question "What is a valid sacrament?"  It went without saying, even in those early days, that a valid sacrament was a sacrament that was dispensed or performed by a validly ordained priest or validly consecrated bishop.  So the question became "Just what constitutes valid ordination or consecration?"  St. Cyprian argued strongly* for what later became the norm for the Eastern Orthodox Church, namely, that for a priest's or bishop's sacraments to be valid, they must be both ordained or consecrated by a valid bishop, AND remain in full communion with the mainline Church.  But, for reasons that have caused many a historian and theologian to scratch his head throughout the centuries, Pope Stephen (the pope at the time) argued successfully for what can be called the "mechanical conception of validity" -- the mere properly performed laying-on-of-hands by a validly consecrated bishop, with no added necessity to remain in full communion with the mainline Church.

The results are obvious, and, to be honest, not always pretty.

But that's where bodies like the NAORC Archdiocese of California have the opportunity to shine, for Christ, and for what independent Catholicism can be when its leaders' hearts are fixed on God and not on matters purely controversial or divisive.

To place the NAORC in its specific "validity context," but without going into too much detail:

Vellone was consecrated by
Verostek, who was (at the orders of Most Rev. Carfora) consecrated by
Bell, whose previous consecration was accepted by
Carfora, who was consecrated by
De Landas Berghes, who was consecrated by
Mathew, who was consecrated by the ancient See of Utrecht (Holland),
which was given the right to elect its own Bishops by Pope Eugene III in 1145, was granted canonical autonomy by Pope Leo X in 1520, and traces its sacramental succession directly to the Holy See in Rome.

The moral of the story is that Rome, by its very own definition, accepts the validity of most independent Catholic bodies which can trace their validity back to Rome itself.  And since the NAORC Archdiocese of California is at great pains to cooperate as much as possible with the Church that gave it its validity, it should come as no surprise why the Archdiocese of California does not hesitate to refer to itself as "non-Papal, though spiritually unified with Rome through Christ."  In fact, it would be the Archbishop's desire to actually bring the Archdiocese of California under Rome's jurisdiction, were it not for the lack of a guarantee that his and the Archdiocese's special ministry, clearly given by Christ himself, would be free to continue as is.

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* The controversy was actually centered on the question "Are the sacraments of heretics valid?" Specifically, if a cleric was excommunicated for heresy, and during his excommunication he administered sacraments, would those sacraments administered during excommunication be accepted as valid upon his reconciliation with the Church? So, since not being in full communion with the Church is heretical, jurisdictionally speaking, the very same controversy can be marshalled in defense of the sacramental validity of  bishops not in communion with Rome -- bishops outside the jurisdiction of Rome, but INSIDE Rome's own definition of what constitutes valid succession, and hence valid sacramental ministry.