Yeah, I can't either. I think the simplest explanation is that no one is completely full of shit and that Kyle simply thought his bargaining position was stronger than it turned out to be. His "you're not going to see me somewhere else next week" was an emotional throwaway statement in the middle of a sincere discussion about how difficult the year honestly was on his family (for whatever reasons) that in light of getting fired (which I'm going to suggest was an outcome he didn't at all expect, knowing as he did that Shanny and the board wanted him back), he's now willing to walk back because multi million dollar paycheques aren't normal.
Basically, he was sincere in what he said