WRONG.
It is perfectly all right to declare a firearm in a checked bag, even with ammo; people I know fly with them, and thousands do it every day. The firearm has to be separate from the ammo, which has to be in "a" factory ammo box (doesn't matter if you just re-use an old one for your reloads), and the whole kit and kaboodle has to be in a LOCKED case that CANNOT be opened by the TSA. Yes, cannot. Otherwise, it is a violation of federal law.
The locked case can be in your regular bag. Again, I know people who do this every week.
Mrs. Nugent's mistake was not declaring a firearm, and not filling out the form.