Holy Mother Church supplies jurisdiction, but (I believe) with the CMRI there is a more profound and wondrous mystery at work:
The CMRI Fathers are totally consecrated to Our Lord through His Blessed Mother, whom the Eternal Father has given the power and mission to crush the head of the infernal serpent and all its minions. She has been predestined to her role of Victress over Satan and the curse of the serpent recorded in the Book of Genesis testifies to this.
Those acquainted with the revelations of Ven. Mary of Jesus of Agreda know that Our Lady fulfilled this office as Protectress of Holy Church after Our Lord's Ascension and the Mission of the Holy Ghost by various victories and wonders kept hidden from many until Our Lady revealed these to her predilect servants in latter times.
Those Priests of this day who are consecrated as slaves of Jesus through Mary, according to the spiritual doctrine of St. Louis-Marie, have been given extraordinary powers in the spiritual order insofar as they have faithfully observed with the utmost rigor of self-abnegation and the selfless generosity of soul the arduous ascetical programme outlines by the same St. Louis-Marie.
Our Lady and her Angels were there with those Priests to deliver that poor girl: the great Mother of God and Mother of the Church never ceases to be solicitous for the welfare of those children entrusted unto her by her Crucified Son in the person of St. John, when He decreed unto this greater and second Eve "
Ecce, filius tuus" (S. Joann. cap. xix. 26).