Similarly, there is real tactical advantage to hide the fact that there is nothing interesting behind the curtain. It keeps the enemies guessing. This is why they say "I can neither confirm nor deny..." (Source: a podcast I listened to)
Also it adds plausible deniability for the times they do have some interesting McGuffin behind said curtain. "Sorry guys, it's just some moth-eaten old folders but gotta follow procedures, ya know..."
As in 'The Art of War': "Appear weak when you are strong, and strong when you are weak."