Inexpensive original 1903's that've been Arsenal Refinished or Updated or Repaired are also out there. They get tossed in with the rifles that have been assembled from Surplus parts by shooters and so are often unrecognized. Any 1903 that is still in its military configuration as last used within the military, whatever that happens to be, is desirable. They too can be considered correct because that was their configuration while last used in the service.
I'm not an expert on the subject by any measure, but there are a lot of guys here on this CSP Forum who certainly are and they can detect original features from those that aren't. I frequently seek their assistance and recommendations.