The message displayed on YouTube.com was instead something that looked like a 404 page not found error message for the Apple MobileMe services (see screen shot below).
The problem persisted for about a half hour (that we know of) and then mysteriously went away.
It may have been a problem with YouTube load balancing servers, since the problem didn’t seem to be reproducible on other computers. YouTube services for other computers, including the iPhone platform, were working fine. It might have been a problem with some DNS servers directing traffic to the wrong location. The actual cause of the problem is unknown.
Below is a screen shot of the error page produced.