I would probably carry, however I would also understand that if found out I would be terminated under this clause or possibly another one they like better. It is up to lawyers and judges to determine what it means. You may or may not be able to win a judgement in a civil court after the dust settles, however you will still be unemployed.
My company has an equally ambiguous policy statement on "weapons". No unauthorized weapons on company property. They neglect to tell us who may authorize weapons per company policy. My manager says we are authorized. Do I know that won't hold up, sure I do. That's how it goes.