It is not really that important, but the barrel date (when the barrel was made) is not necessarily even close to the rifle assembly date. Since the barrel making process was more automated than receiver manufacture and assembly, the date when the barrel was made sometimes ran months ahead of rifle assembly. Further, barrels were made and racked, then taken in no special order for assembly. So LIFO was common, with older barrels staying behind for long periods.
Also, needless to say, when a rifle was rebarrelled, no attention whatsoever was paid to either the barrel date or the manufacturer. For some strange reason, ordnance shops in WWII didn't worry a lot about the concerns of collectors seventy years in the future.
Jim