SA received left over receivers from RIA post 2020. In 1919 SA still manufactured 1903 rifles themselves. It would not make sense for them to assemble a RIA receiver with an Avis barrel. Whoever told you this is wrong. I fully agree that you will never find an original NM rifle with an AV marked barrel. Except for 1919 ALL NM rifles were made exclusively by SA. And SA NEVER used any other production barrel, except for their own, for the National Matches. The RIA NM rifles from 1919 all have had RIA barrels.
Hopefully jvbeard will join this topic, he can tell you much better than I can.