Bingo, you have it correct.
Do not over think this, they sure as hell have not and above all else, when interpreting what the ATFE says in their rulings you must remember this above all else, LOGIC is checked at the door.
For shits and giggles, let's revisit the second vertical grip on a pistol fiasco for a moment.
ATFE definition of an AOW says if it has a rifled barrel by their own definition it cannot be an AOW unless it does not look like a firearm, such as a pen gun or pager gun (recently added).
But, the ATFE has ruled that by putting a second vertical grip on a handgun makes it an AOW because in their eyes putting the second vertical grip on it makes it no longer fit their definition of a handgun, which says a firearm with a short stock designed to be shot with one hand.
Let's see, on one hand they say it cannot be an AOW because it has a rifled barrel. On the other hand they say that putting a second grip on it makes the gun not shootable by only using one hand even though the true design of the gun has not changed by adding a removable second grip.
The definition of a handgun does not say anything about not being able to use two hands but they sort of, kind of imply by their ruling (using their twisted insane logic) that if the gun allows the use of two hands then could it be an AOW? How stupid is that? See, logic has nothing to do with ATFE rulings. My 4 pound .50 Alaskan Encore with a forend mounted bipod is a handgun, but if I remove the bipod and put on a forward vertical grip it is an AOW??? But the wooden forend that allows a second hand hold is OK because it is not perpendicular to the bore. A second grip parallel is OK but one perpendicular is not?
And what really makes this ruling so insane is that just this past year the ATFE redefined what an AOW is, and they could have included the second grip but they omitted that, instead only including firearms that do not look like firearms such as the aforementioned pen guns and pager guns.
If you try to make logical since out of what the ATFE says you will yourself go insane.