to the contrary

Rhetoric to the contrary notwithstanding, these new mandarins will stay resolutely wedded to the necessity of American unilateralism, their guiding precept being “unilateralism whenever possible, multilateralism only when necessary.”

She hadn't had "any surgery until recently... only fillers", she told Atwood, despite speculation in the press to the contrary.

You will be told, despite evidence to the contrary, that everything is better than ever.

Russia denies all allegations of war crimes in Ukraine, despite well-documented evidence to the contrary.

A case of massive oppositional mendacity that borders on the hilarious — except that many people believed and continue to believe him, all evidence to the contrary.