The Church enjoys a close relationship with the university's education faculty, the only training base for Catholic teachers, and pinned its faith in a diploma course to provide a Catholic "pathway" other Scottish Qualification for Headship courses did not.
But Bart McGettrick, head of the faculty and a commission member, backed the integrationist approach, although it is alleged he is out of step.
Professor McGettrick told The TES Scotland: "We do not wish to see programmes differentiated by school type, such as denominational or non-denominational or small school or large school. My belief is to continue to see Catholic education working with the grain of Scottish education and to improve the grain if necessary.
"What I do not think is in the interests of Catholic education is segregation or division. I believe the ministerial judgment can be accommodated, along with the views of the Catholic community."
However, John Oates, the commission's field officer, labelled the ministerial diktat as "inadequate and inappropriate" and warned of "wide-reaching consequences".
"The minister has clearly shown that he does not really understand what Catholic education is about," Mr Oates said. "He has said his door is always open but in the meantime all Catholic references will be removed from the course in the faculty, specifically set up to support Catholic schools. That is not a good model for partnership in our view. There is also the question of academic freedom."
He added: "The headship qualification is a technical, professional qualification and does not take into account the principles of Catholic education and does not trainpeople to be headteachers and leaders in Catholic schools."
Sam Galbraith, Children and Education Minister, wrote to the university last week following his clash with Catholic secondary headteachers at their conference in Crieff. He refused to buckle under stern pressure to accept that depute heads needed particular training because of denominational schools' special mission.
Mr Galbraith also wrote to Cardinal Thomas Winning, setting out his concern about labelling courses. He is adamant that all aspiring heads share similar training needs, although he accepts the Catholic dimension could be an add on.
Catholic heads, however, expressed vehement opposition to an add-on scheme and demanded that training for deputes be integral. "We want something that permeates the programme," Mr Oates said.
Michael McGrath, head of Our Lady's High, Cumbernauld, said he had received no "reasoned argument" for refusing their plea. "We want our headteachers to be able to articulate a vision of Catholic education that is explicitly religious in purpose and built round the reality of political, economic and social priorities. We can do both.
"We have no wish to establish a separate SQH for Catholic teachers. But we do wish to see our particular needs acknowledged by the authorities who have a duty to provide appropriate support to Catholic teachers."
Professor McGettrick replied that deputes would probably have been working in the sector for 20 years or more. They would have been trying to understand aspects of leadership, management and finance in the context of a Catholic school throughout that time.
It was "absolutely essential" the faculty's course was unified and nationally accredited. "In a sense, there has never been a Catholic pathway if it means a separate identifiable programme," he said. 'The minister has clearly shown that he does not really understand what Catholic education is about'