Actually, Mel did have priests from the Legionaires of Christ on the set. I don't know for a fact that they offered Mass, but they may have celebrated the New Mass separately from the Latin Mass that Mel attended. I'm pretty certain that Cavaziel attended another Mass.
The priest who most often offered the Latin Mass on the set of "The Passion" was Fr. Stephen Somerville. He is a priest from Canada who back in the sixties and seventies had been a member of the ICEL committee that wrote the execrable "translation" of the Mass. In the recent past he wrote a public denunciation of his own service on the committee and renounced any support or approval of what was done with his assistance. He has since become a "cooperating" priest with the SSPX.
Renouncing My Service on I.C.E.L. - An Open Letter - by Father Stephen Somerville, STL
His is a common situation. Others that come to mind are Fr. Stephen Zigrang and Fr. Lawrence Smith, both of whom left their diocesan assignments last year to cooperate with the SSPX. The SSPX is a fraternal society of priests, similar to a religious order, and only certain priest are official members. But there are many other priests both religious and diocesan who cooperate by offering the traditional Latin Mass at SSPX-associated chapels.
Wow! Bookmarked. And thanks for sharing this.