I'm missing something. Where does your quote mention that Gibson attends SSPX Masses?
In researching Mel Gibson's mass attendance, no one resource specifically used the acronym SSPX. USAWeekend writes the following:
"As for his religious beliefs, Gibson, 47, a father of seven, is a member of the conservative traditionalist Catholic movement, which still celebrates mass in Latin. He's also the financial backer of a church called Holy Family, being built near Malibu for a congregation of about 70. "
Do you suppose this is a FSSP congregation? Do they maintain their own churches? According to the FSSP web site:
"The main work of the Fraternity of St. Peter is the operation of pastoral missions throughout the United States and Canada, for it is in the parish that the souls of the laity are formed and nourished in the sacramental and catechetical life of the Church. The Fraternity currently operates apostolates in over twenty North American dioceses."
The fact that they are operating at the diocesan level, would suggest to me that they are working in diocesan churches. Which brings us back to Gibson's construction of a church. Who authorized him to do so? Who will bless it and consecrate the altar? Isn't that normally the function of the bishop?