In Visit to a Small Planet, why is the whole situation turned over to Paul Laurent? Who is he?
Two other technical reasons come to mind as well.
For economy of style, the characters are all stock characters or stereotypes, none of them very well developed. The play being very short, there is not much time to get into the nitty-gritty "whereofs and therefores" of the story line, or even to make it seem credible. Even Kreton does not change, only the spectators' understanding of him. Laurent the diplomat does what a diplomat does - he represents a whole, and that's it.
The sparce characterization in this very short play enhances its literary genre, the farce. Characters are intentionally underdeveloped and are not to be taken seriously. The focus is rather put on their comical juxtaposition or confrontation, as often is the case in a comedy of manners.
In Gore Vidal's play Visit to a Small Planet, Paul Laurent has authority because he is the Leader of the country, which is the reason General Powers and his Aide stand at attention, although "President" is never used. Additionally, Laurent speaks in the name of the World Council (i.e., United Nations) either because he is the leader of the World Council or because he qualifies as their spokesperson, seeing as how the UFO has landed in his country. This is who Paul Laurent is and his identity should explain nicely why he has authority to decide and act: As the Leader of the invaded country, his is the Commander in Chief and therefore invested with such authority; as the spokesperson of the World Council, he holds similar authority, though of course it is not unilateral.