My guess is that he was so taken at the honor of a Homeland Security officer visiting the plant that he forgot to use common sense, or perhaps he just wasn't too bright to begin with.
There was an addendum to the story on Quayle's site whose source I don't understand, but it states states "Guy calls BASF Chemical Plant in Chattanooga and starts asking a bunch of questions and says he's with Homeland Security. They told him he'd have to come in because they couldn't answer his questions on the phone. 3 days later the guy shows up in a "uniform" and packing a gun. Asks BASF all about their operation, he was really interested in the rail cars that enter the plant with tanker cars. Asking the schedule of them, if they can be rented and other various things. The stupid people never checked him out and told him everything he wanted to know. Days later the real Homeland Security had contacted them about uping security at the plant because of possible terrorism etc. And they said yeah one of your guys was already out here..."