The Pentagon is often used as a shorthand way to say the Department of Defense or even “the military.” This is a textbook example of metonymy.
This may very well be what’s going on. If it is, clicking on the two links I compared above should show why I was confused.
The Rumsfeld pic is interesting – the backdrop says “Pentagon: Washington, D.C.,” but the Pentagon is not in Washington. It’s in Arlington, Va.
Also note that on the front of the lectern is the seal of the U.S. Department of Defense.