Eh, I'm not sure that's a good way to look at it. It wouldn't change the BATNA because the BATNA is the state you are in if no deal happens.
Pareto and KH are about the outcomes of a deal. Kinda like evaluating the opposite of the BATNA, if you will. It quantifies the improvement of a deal over the BATNA, and you should accept when you cannot manipulate the deal to improve your outcome. Sometimes, those concepts are used to refer to the OVERALL position of all parties, meaning that everyone is getting the BEST deal possible (maximum improvement).
As I've always heard it used, KH is used to describe the overall state, while Pareto refers to individual parties (could be my circle of experience though, as an attorney I don't deal with too many people who regularly think in these terms).
My question was about whether Peyton's involvement changed the entire landscape, meaning that when he got involved brand new Pareto improvements were possible - thus making the previous landscape non-KH efficient.
Hopefully that makes sense.
* I could be very wrong in the way I use these terms. I'm a lawyer, not a business professional.