Tom, to further illustrate your point, we could also note that at the end of the war, the French sent 13 ambassadors to the united states - one for each independent nation.
The modern United Arab Emirates provide something of a moderately analagous example of how the U.S. was viewed internationally in the early years. As with the UAE (in theory at least), the United States (in reality) were totally independent states that chose to function as one entity only for the purposes of international diplomacy and trade. The "union" of states extended little farther than that.
As far as your reference to the use of the plural, note the grammar used when referring to the UAE at the wikipedia site: "...the UAE were known as..." just as one might say "the US were granted independence by the treaty of Paris..."
