Right. Doesn't that make him British? Asking honestly... How could he have been American if the USA didn't exist yet. Obviously he was North American, but his citizenship at birth would have been British, no?
As you can see, this covers the corner case you've identified.
Interestingly, the term citizen wasn't defined until the 14th amendment: "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside"