The paperwork issue is very troubling.
The majority of weapons I've seen advertised as "bring backs" were missing the paper. Understandable, since it was only useful to get the rifle on a plane back to the US. I don't imagine that many GI's would have thought that they needed to preserve it to prove anything later.
I've got a ChiCom Type 53 carbine with no paper that I bought from an Army buddy in 1983. He had been in the 173rd ABN Bde. in VN. I know it is a genuine bringback, but I could never prove it.
As mentioned earlier, it is possible to fake the paperwork, too, not only for VN, but for WWII also. There was a man on another gun forum recently selling original, blank Army registration forms from WWII for war trophies. He wanted buyers to email him directly instead of posting in the thread (for anonymity?). I doubt there are many blank form collectors out there, and it's easy to presume that someone has other plans for their use(?)