He's too much of a control freak to let Caster do these raps without knowing what's being said, if he goes over them when they are on Dynamite why would he just let them say whatever they want without going over it on Dark? He's there when the show is taped, he'd have to be an incompetent fool...well that's a possibility lol. They should have just said nothing and let it blow over, only a small hand full of people were complaining and it was nothing a day or two later.He clearly knew but this is what he does whenever they get negative press. Gets defensive and claims it was all down to other people and claims something different will happen going forward.
And like you said it happened 6 days before it aired so I doubt no one bought it to Khan's attention if he didn't somehow hear it at he time.