That article has a lot of errors, but the basics are correct. The M1903 was based on the Krag and the Model 1893 Mauser (not the Model 1898 Mauser) and was made at both Springfield Armory and Rock Island Arsenal; except for markings the guns from both factories are identical and parts are interchangeable. 372xxx would have been made about September, 1918.
FWIW, the so-called "low number" cutoff for RIA was 285500, so 372xxx is well into the double heat treated range.
Jim