I did notice in further testing that some of the Connected Media items do behave this way. I think it is a bug, but those Connected Media items aren't working right anyway. It is essentially just playing the audio inside MC's internal browser. This stinks because you don't go through MC's audio engine then (it renders it through the embedded browser's engine), so you don't get DSP and internal volume control or any of that stuff.
If you play the PublicRadioFan streams, you'll see how MC is "supposed to handle" the playback. It happens directly in MC itself, and MC controls the audio. For these, it will keep playing if you go to Playing Now, and visualizers work and whatnot.
For others, like SomaFM and Icecast, I'm seeing the behavior you're describing, but they're broken anyway. Some of them, like SomaFM pop up a separate browser "pop-out" window when you start playback, and after you close MC they keep going, but if you close the pop-out window, then they stop. Others, like the Icecast feeds, do indeed keep playing when you close MC's UI.
That's annoying. But those Icecast feeds aren't working the way they're supposed to anyway. They should work the way the PublicRadioFan ones do, but something broke.
Either way, it looks like the browser-based playback isn't stopping when you exit MC. I bet you can replicate it with YouTube as well.