The RIAA makes many assertions. Whether they are enforceable, or even the correct interpretation of copyright law, is a separate thing.

It could be difficult to enforce requiring a performance license in an office, but I suspect alleged violators if caught will settle rather than let it go to court. Of course, this then proves nothing.

That being said, I would say they're probably right, because it doesn't seem that different from a store or restaurant playing music.

If I play it at my desk it seems very different than the office piping it out to everyone as 'background music.'