"Baptism by desire" just requires whatever is going on in the soul of a person (a non-Catholic, for instance) and the ministrations of God's grace. No human agent or bureaucratic administration is in control of dispensing grace. "The Church" which is present in the "salvation" of such a soul is "the Mystical Body of Christ." Ecclesiologically speaking, "the Church" should never be confused with whatever earthly institutional structure happens to be representing it. It's a reality much more than that. Quite beyond the external corporate structure of any congregation, parish, diocese, bishops' conference, etc. Clericalism is not "the Church."
There is sometimes an eschatologically hubristic tendency for individual clergymen to think that they alone are "the Church." This is wrong. Since none of us are ever present in a situation to know the condition of a soul when a person actually dies, no one living knows who is ever saved or damned. Only God does. It's great whenever very holy Christians manage to mature into wise, loving, and devout clergymen. Since this is not always the case, obviously the mystical/invisible/spiritual dimension of the Church, the communion directly between God and souls, has priority.
Amen to that!