I am responsible for signing off on all clearances in my building. The research labs here are a simliar area to your scenario. Here the approval process is a little different - the employee is responsible for getting the form from me, then securing the signatures for approval - i.e., the people in charge of the lab, then bringing the form back to me. If the researchers sign off on it, then I put it through. I've had the occasional "But I slid the form under your door when you weren't there" person - whom I then give another form to, and who can't secure the signature but were just trying to get me to put it through without the documentation in my hand.
Could you change your system so that any given employee has to get his supervisor's written approval to particular areas before it is submitted to you? Or develop a check off form of verifiable reasons why an individual might need access to an area or a particular door?
Another example - our loading dock is a more convenient exit than the regular doors for many employees. But I refuse to give access just because it's more convenient. They must have responsibilities which take them to the loading dock. I tell them it's a liability issue because it is a loading area. I've never been told that for a fact, but I'm sure I could back up the argument if need be (i.e., no railing to prevent one from walking off the edge of the loading dock...).
I'd like to hear how your scenario turns out.
DonnaP99