Clearly, he does not represent the United States. If he did, that would be a strange system of representation. He acts as an individual, but one with the prominence that might indicate an ability to get something done. He doesn't have to respresent us to make progress for/with us.
In fact, it's quite convenient. Of course, we American's don't negotiate with terrorists. But other people not affiliated with us can negotiate as a proxy. Thus we can both remain aloof of diplomatic concessions while, effectively, making them anyway. And also, Carter makes for a convenient scapegoat (if things don't go well), or for a convenient leader (if by a miracle, they do).
Edit: Posted from the wrong account. I don't mean to "..."
