Ah, but if your neighbor's stereo is faintly audible in the distance while you record a screencast, your video will get taken down off Youtube very quickly.
Do it with a private video, it won't be taken down.
I guess they've since changed their policies.
From a copyright perspective there's no issue with uploading your own personal videos with copyrighted material in it to a site like YouTube so long as they're still private. I guess YouTube just assumes if you're uploading it there, you're going to eventually want to make it public. IMO they should just show the results of their scans to clue you into potential copyright claims but not actually do enforcement if the video isn't available publicly.
Note: an unlisted video is still a public video.