To lure people into coming back, I proceeded to step two of the master plan - posting a YouTube video on said blog. I upload the video, make it private, select the radio-button labeled "Enabled: External sites may embed and play this video", embed the code in a post, and check the blog. The video is there, and I am very proud of myself.
Well, not for very long. The next day, I conspiratorially tell a colleague to check the blog. The nice YouTube thing is there, the colleague clicks on the "play" button, it begins to load, and... keeps on loading, forever.
I found only one way to fix the issue - making the video public. It would seem that embedding a private video works, as long as the viewer is logged into YouTube with his account and added to the authorized viewers of the video. Maybe I am missing something here - but if not, you really have to wonder why the "enable embedding" option is provided at all. And the worst has to be that videos appear exactly the same, regardless of whether or not a user is authorized to access them - and giving no other way to find out than to wait for the load to fail.
Hopefully, YouTube will become better integrated with Google's existing suite of services over time, with a more consistent behavior; in the meanwhile, I will check back Google Videos for comparison.