I suspect most of us are either watching it rain, or worse SO I re-discovered an article that Joe Wood sent me long ago from American Rifleman Nov. 1937 by A.P Curtis "Making Double Shotgun Barrels":
"Tubes having water tables (he used two words) are machined and barrel lugs and extensions assembled, and all brazed together into one unit."

If Curtis called the barrel flats "water tables", that would seem to indicate they serve as a datum.

He also mentioned the American Gun Barrel Company of New Haven, Conn. making barrels for the U.S. market 1914-1921, but it could not compete with the duty free importation of tubes after Belgium recovered from WWI.

AND that Hunter Arms made the first barrel straightening machine in the U.S. in 1909.

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