After over 60 years since the M1903 was used as a service rifle, it would be hard to tell where it came from. Possibly, a former civilian owner changed the stock. During overhaul, most no- or one-bolt stocks were discarded or modified to two-bolt configuration. An early stock usually has a small or lage "S" stamped on the foretip, which would tell the likely source of the stock - small, SA; large, RIA.
I agree it is likely the barrel is original.