There have been some odd answers here, but the last was correct. All replacement barrels are "short-chambered" that REQUIRES fine reaming of the chamber for correct final headspace. There is no extra turning of the barrel further into or out of the receiver!?!? This is not a practice in any respect. As long as the barrel is properly aligned and the barrel thread shoulder is flush with the receiver face with about 35ft/lb torque (if I remember correctly) the only issue is the condition of the chaber itself. Headspacing requires a special reamer easily acquired at a reasonable price, but its is unfortunately easy to cut too much (learned from sad experience).
The rifle may be a parts gun, but it may also have been arsenal reworked but never finished not final proof fired...unlikely, but possible. In any case the replacement barrel and replacement scant stock was not an unusual practice in WWII or post war arsenal rework/repair (see Harrision's or Poyer's reference books) as both such barrels and stocks were in arsenal inventory by that time.
Lsdtly, there is nothing wrong with "parts guns). As long as USGI parts are used and especially if matched for type (version) and mfr. Unless there is written provenance attesting to it being either (parts or arsenal reworked) there is no way to quantitatively verify that is wasnt arsenal reworked.
In any case a properly assembled 1903 parts gun yields the exact same result as an arsenal reworked rifle, and generally built from the same spare parts inventory, so...enjoy!