Unfortunately, the archbishop cannot control private corporations just because they have “Catholic-sounding names.”
The best he can do is demonstrate moral authority, which is what he is doing.
Hence my question wondering about the distinction. If it is *not* a private corporation, and is, in fact, an arm of the archdiocese, then he could stop the show, period. If it is not controlled by the archdiocese, then, clearly, he does not have the power to stop the show outright, and he has done the best he can. However, this second scenario underscores the problem of having Catholic names associated with secular outfits. Both Archbishop Burke and the rest of the Ordinaries of dioceses might want to look at this situation and insist that secular concerns and foundations divest themselves of Catholic terminology in their names.