That pretty much sums up my understanding of rifles in the service. I believe the overwhelming majority of so-called "bringbacks" are when the veteran obtains a rifle like he used from another source, like a gunshop or sporting goods store. The story may start out as "This is like the rifle I used in (fill in the blank) war". Over the years, the veteran (or his relatives, after he passes away) may gradually change the story to, "This is the rifle I carried in ______ War."