Oh, puhleez, Scorch.
The Luger was patented in 1898. The Swiss adopted the Luger in 1900 and the US Army was testing Lugers in 1901, with commercial models selling alongside. John Walter says that at the time, half of DWM's production was going to America.
Five years from 1903 was when the German Army finally got around to adopting the P '08. The German Navy had been using them since 1904. Not an uncommon thing in those days, for many years most navies were technologically ahead of the corresponding armies.