When I first started work as a government contractor in the late 1980's, the government badge had a different background for employees with security clearance (they have since changed that). We were warned that it was a security violation even if we didn't have security clearance to wear our government badge in public, because a foreign operative could tell what our security clearance was just by looking at our badge.
Point is, that it is actually a security violation to reveal anyone's level of security clearance, even to say that they have none.