Christ humiliated his apostles in public?
This is basic human skills management: don't humiliate your employees in public.
Your example doesn't work, as this priest is a brother to Olmsted, in the clergy, and Olmsted is acting, with all due respect, like a bully. Paul said that correction should first be made in private.
If you think this is the way to work with people, you've obviously never been a manager.
As the character of Thomas More said to Cromwell in "A Man for all Seasons":
"Terror is for children. Not for me."
So whether or not the Bishop confronted them in private, to confront them in public given their previous public stand would be entirely appropriate.
Besides I'm not sure this bishop see these guys as true servants of the church. He may very well see them as infiltrators. If you are trying to get a disruptive employee to resign, and make an example for the rest of your employees. You might very well call them down in public.
Why don't you blow the dust of your bible, sinky?
Yes, Christ humiliated his apostles (and followers) in public. "Get behind me, Satan....", "Put your finger in my hand, Thomas .....", also John 6, where a whole pile of Christ's followers left after their public humiliation.
Your liberal AmChurch touchy feely egoes are just TOO BIG to fit in the confessional, imo.
See the second link in 'Phx-RC's post #3 from the Arizona Republic. This is the first sentence (bolding mine:
"Bishop Thomas J. Olmsted privately has ordered nine Catholic priests to withdraw their support from an interfaith statement supporting gay rights."
These Priests released (or gave the gist of) the letter publicly, not the Bishop.