Okay, found this quote from the Sipsey Street Irregulars blog (did a Google search):
...In response to a request for clarification of the law, ATF advised a firearms manfacturer in a letter dated July 20, 2010
" . . . in an effort to achieve consistent application of the law, ATF utilizes 26 inches as the presumptive standard to determine whether a firearm is 'capable of being concealed on the person' [and] "barrel length is considered only to the extent that it constitutes a portion of the overall-length measurement of a firearm."
OKAY, so an "AOW" must be a concealable weapon, and ATF has said that under 26" overall length IS concealable (you could hide it under your arm while wearing a coat).
But ATF apparently also says that no matter how long the barrel is or the gun's OAL is, if you do in fact conceal it, it is an AOW. If it's a smoothbore weapon that does not meet the definition of a regular shotgun, and you conceal it, you've proven that it's "concealable" and therefore an AOW.
(This is quite inconsistent with what BATF has said about using the buffer tube on the back of an AR-15 type pistol as a sort-of de facto shoulder stock. You can use it as such, as long as you don't modify it to look like a stock or function as a stock.)