As a cardinal, Cardinal Burke has faculties to say Mass whenever and wherever he chooses. The local bishop has no authority at all over him. The fact that he chose to respect the wishes of the local bishop shows what a classy guy he is, and the pettiness of those who resist the Extraordinary Form, no matter their position.
I'm not sure this is true under Canon Law. The Bishop controls the faculties of priests in his diocese, and he can grant and suspend priestly faculties at will. The same goes for an Abbot.
As Cardinal, Burke is not necessarily this Abbot-Povost's ecclesiatical superior, on the Abbot's own territory.
Nevertheless, what this Abbot did was obnoxiously insulting. Burke has been singled out for public humiliation. THis --- and his equanimity, his refusal to lash out --- makes me think God is choosing him to be a great saint.
I still think Burke could be the next Pope.
Oremus.