Hi Matt,
I can definitely reproduce this issue 100% of the time. Pressing the 'Stop' button on my Logitech G15 keyboard will cause this. Using the other buttons (i.e. Play/Pause, Fwd, Rev, etc...) has no effect. And it's only when Media Center 14 is minimized to the task bar.
If I can think of anything else, I'll be sure to post.