If arbitration is a negotiation, then so is a court case. Making your case to someone else, whose decision you've agreed to accept, and who then decides, doesn't seem like negotiation to me; neither does going to conflict-resolution mechanics in a game--especially not combat resolution. There is a reason I have compared going to such rules as arbitration. And if those doesn't seem like negotiation to me, they're going to seem even less like negotiation to someone who is "precious" about their GM authority.Your definitions are correct, except for the claim that these aren't kinds of negotiations.
OTOH, you seem willing to describe any attempt at conflict resolution as "negotiation," which ... is gonna lead to a circular argument, which is silly because except for that word I don't really have a problem with the quotation.