Every time I hear the phrase “under oath” I mentally replace it with “pinky promise” because it all has tbe exact same amount of weight. There’s no reason to assume someone is being truthful just because they promised you they aren’t lying.
Then there is the technicality of “if they believe it is the truth then they aren’t lying” so as long as other have convinced them enough for them to believe it, then they haven’t broken their oath.
This is just meaningless elementary school behavior from adults and anyone that can’t see that or thinks oaths and such symbolic social constructs are meaningful are not worth taking seriously.