Well, "The Keys" include the authority to regulate who will and won't be priests, who can and can't offer Mass in a particular Diocese, who is and isn't a priest in good standing. Anything else is antinomianism, imo.
The rent-priests used to subscribe to such Divinely-Constituted authority and they used to be obedient to it. Recall the Evangelical council to obedience ?
One characteristic of a man stricken by Pride is his refusal to be obedient to legitimate authority. Many reasons can be advanced to rationalise one's refusal to obey, but one favorite one is to link one's will with God.
In disobeying Divinely-Constituted authority, I am really obeying God.
Luther-lite is unattractive. I wish they's just say "I stand outside the church." However, it takes a man to say that.
915 Christ proposes the evangelical counsels, in their great variety, to every disciple. The perfection of charity, to which all the faithful are called, entails for those who freely follow the call to consecrated life the obligation of practicing chastity in celibacy for the sake of the Kingdom, poverty and obedience. It is the profession of these counsels, within a permanent state of life recognized by the Church, that characterizes the life consecrated to God.454
916 The state of consecrated life is thus one way of experiencing a "more intimate" consecration, rooted in Baptism and dedicated totally to God.455 In the consecrated life, Christ's faithful, moved by the Holy Spirit, propose to follow Christ more nearly, to give themselves to God who is loved above all and, pursuing the perfection of charity in the service of the Kingdom, to signify and proclaim in the Church the glory of the world to come.
Besides the excellent points you have already raised Bornacatholic, I would also add that these men have broken their vows before God that they swore they would uphold to serve God and the Church.