I run Windows Live Care on all my home machines so I thought maybe that was it. I granted exceptions to YouTube.com and tweaked every setting I could imagine. After not getting anywhere, I tried just shutting it off. And of course, nothing. I rebooted over and over, flipped off and on every setting I could think of, and none of them fixed the problem.
After searching around, I found that the problem is that the download link specified doesn't install the Full version of Flash. So you need to simply install the full version of Flash and viola. Why that's the case is beyond me. Here's the link that tipped me off to the solution