My theory: the original story was fabricated, either by Korir or one of his stringers, and they were caught by surprise when the story, which normally would have been read by his couple of hundred Africans in Norway readership, went viral. At that point, he has to either 'fess up or dig in and hope for it to go away. He's done the latter. If he can stall until next Tuesday, he figures no one will care anymore, or he'll come up with some other story about why he's permanently sealing the tape or somesuch. I'll put money on this.
If you think about it, why would Mrs. Obama bother to talk to small fries like that for so long.
The suggested 45 minutes of tape itself seems illogical to me.