noofy - I agree with you. Using the existing rules should work 99% of the time, allowing everyone involved to narrate a satisfying fictional result to one (or more) party member's betrayal of the group.
However, that other 1% of the time, when two (or more) PCs are warily circling each other with drawn weapons and preparing to spill each other's guts on the cold, hard ground? At that point it's going to be up to the GM to tweak the rules slightly so that neither PLAYER gets upset at the outcome. Sometimes, and I emphasize "sometimes", we're just going to need some sort of balance in this kind of encounter.
Whether or not this sort of encounter actually ends with the losing PCs guts spilled on the ground is still something that can be narrated within the rules. Yes, definitely, the winner may decide that using Parley as his "damage" is more satisfying, or maybe he has another idea and comes up with a custom move on the spot.
And let's not forget the "Last Breath" move. Specially when there might be a god looking on, waiting for some reason to step in and prevent something really bad from happening.
There are lots of ways that the fiction can take over again, but the actual "duel" between the PCs should provide both players with the opportunity to "win."
In the end, this is a game with shared authorship where everyone, not just the GM, should be a fan of all the PCs. Is it bad to have a special rule (or suggestion, or hack) for a situation that might otherwise sour the game for some players? You might never use this hack, but it might be something that other GMs would use. Or, at least, something that other GMs might hack even more.
I think, when it comes down to PvP, perceived fairness is essential when there's a possibility that one player might come away feeling cheated or otherwise soured on the game.
YMMV. Ours, too, as we get more experienced with this system. :)