If that was the case the snake guns made by Crescent and H&R would be legal.
Good point; I think it would depend on whether the Remington was a very uncommon special order, and then it would still be up to BATF to say "yea" or "nay."
Like I said, the S&W 9mm carbine is very definitely an NFA weapon by BATF's definition, yet they removed it from NFA status, even though it's got a 10" barrel.
The primary difference between the H&R Handy Guns, Ithaca Auto Burglars, etc., is that they were common production weapons and thousands were produced.
I suspect in this case, however, that the shotgun was chopped at some point in its life, and therefore the OP should run, not walk, away from it.