Confused about "I can’t in good countenance continue..."

Taken from the article's title in Independent:

Fox news cuts away from McEnany press conference: ‘I can’t in good countenance continue showing this’

As I understand it, countenance means facial expression. So in this case, the title's meaning would be, "I can't with a straight-face continue..." or "I can't continue composed..."

Do I have that right, or would the phrase "in good conscience" be more suited here?

It seems likely that Cavuto blended the idioms "in good conscience" and "cannot countenance".

You couldn't, in good conscience, ask her to pay the whole bill! (without feeling guilty) -Cambridge

Jake would not countenance Janis's marrying while still a student. (do not agree with it and will not allow it to happen.) -Collin's

'countenance', as a verb, means to admit as acceptable or possible, to tolerate, to permit, to put up with; so Cavuto could have said, "I can't countenance (what she said)", but introduced by "I can't in good...", it needs a noun, not a verb, so "conscience" would be the expected phrasing.