I am unable to comment on the authenticity of your star-marked barrel sans star gauge record number. I can, however, point out that January, 1922, was the beginning of a new series of star gauge record numbers that were marked in a single line and preceded by the alphabetical letter "B", the first of which was simply "B". By 1923, the B-prefix barrels became exclusive to NRA Sporters. I will also point out that NRA Sporter barrel star gauge record numbers were usually stamp midways of the barrel and sometimes on the bottom of the barrel. So I recommend that you examine the barrel around the midpoint for a 1 or 2-digit number preceded by the letter "B" and perhaps a hyphen.
I concur that star gauge inspection was used to control and confirm the quality of barrel manufacture. But barrels exhibiting a star gauge record number were actually barrels specially manufactured for the National Matches.
J.B.