Hypothetically, lets say you are trying to record something off youtube or your media player. Could you not just select the browser or player with the 'Rectangle Capture' option? Resize and relocate the rectangle so it fits on top of whatever video you are trying to dupe, then start recording. Play your video and baym, you 'should' have just nabbed yourself a free song off youtube! Or something, I don't know.
If you don't know how to do this; when you run Debut there should be a 'Capture Snapshot blablabla' icon with a little photo camera. Above that, four more icons. The one of the right lets you change what part of the screen you record. From there, doubleclick on any window you want to zone in on. Or manually resize it.
Hope this helps, and that I'm not missing some flaw that prevents recording youtubes and the like :/