Its been a long time since I read the history on this case. My memory may be fuzzy or inaccurate,so do your own research.
Your fuzzy nutshell description leaves out a number of very important details, and gets some others wrong. However, I don't feel this forum is the proper place to discuss the details of that case. PM me if you want to discuss this matter further. The case was settled, monies were paid, Weaver did not go to prison, and the government "admitted no wrong doing".
As to the short barrel guns being sold today, being ATF "approved", ok, fine. What is, and isn't approved by the ATF has changed many times over the years, and could change again further down the road.
Remember, what the ATF giveth, the ATF can taketh away. And they have a history of doing so.
If you do get one of these new 14" barrel guns, be prepared for a hassle (and possibly some expense). Every city, county, state, and Federal cop KNOWS that short barrel shotguns are illegal.
Even if you have the approval letter ON YOU (and I recommend you do have it on you when ever you have that shotgun on you..) that doesn't mean your gun, and likely YOU, will not be seized.
MAYBE the officer will let you explain, maybe even accept your explanation, (and the letter) but they don't HAVE to. It is very possible you could spend a night, or even a weekend in jail, before you get to see a judge.
Do avoid arguing with the officer, and anything that could be construed as "failure to comply" or "resisting arrest". Even when the gun charges get thrown out, if you resisted arrest, that won't be thrown out, and you could easily wind up convicted, losing a great deal more than that shotgun. Maybe, for life...
Don't expect to be able to recoup any legal expenses this causes, either.
And, don't expect to be able to make your own copy of the Remington/Marlin 14" either, even if its a perfect copy, exact in all dimensions, you will be facing jail time over that, UNLESS you get the tax stamp and approval BEFORE making it. The law has quirks, about things like that. ALSO, better check your state laws VERY CAREFULLY. Just because the Fed says its ok, doesn't mean your state does.