Lets see this improper documentation. If they have it, they ought to put it on the website for all to see.
You say they probabbly do it routinely? Maybe they dont? Is the document the same for all airlines? Has this agent ever flown American with his weapon before? Was the pilot being picky (i.e, no signature as reason for rejecting the improperly filled out form - pilot sounds worse than an IRS agent).
IMO, considering what AA has been through since 9-11, they were well within their rights to deplane ANY and ALL that made them or their passengers nervous.