Lena, nothing personal, but your theory is on the same level as the artificial fog.
The President had onboard members of his staff and PAF commander who was, we may say, his protege. He wasn't going to storm into the cockpit and discuss anything with a simple captain. I will not mention things like the chain of cammand. Sorry, but there is no mystery here.
I have something else.
It was easy to hear the GA form the FO on the CVR, but in the case of the PIC, phonoscopic analysis was needed. Why? The placement of the microphones in the cockpit is symmetrical.
Arrakis