I wonder how many of the allegedly "German" immigrants to the USA were actually
Austrians or Schweitzerdeutsch? I suspect a great many of these were labelled
"German", from the language they spoke, just as most Flemings were labelled as
"Dutch". My mother's ancestors, who emigrated to what was then New Amsterdam,
was always seen (in the family, in later centuries, at least) as Dutch/German.
An analysis of the names indicates that it was really Flemish/Austrian.

Or am I splitting hairs?

Harry Needham
Canadian War Museum