YouTube was tiny in comparison when Google bought them. They did an admirable job scaling to where they did, but it wasn't easy and it was still jut the beginning. They served ~100M videos a day and today serve over 3B videos a day (many in HD, which wasn't supported in 2006, the videos then were much lower quality). The amount of incoming video has also grown exponentially.
The YouTube we know today is because of Google and their technical chops.
OK, but the only reason (as per the post I was responding to originally)?
Those ~100M videos a day were about 99M (I'm guessing here) more than Google Video was doing at the time.
I believe you that Google's technical prowess was a necessary condition to get YouTube to where they are today, but I find it hard to believe that YouTube did nothing whatsoever to warrant becoming the original name brand of web video in the first place.