I'm pretty sure that was the primary reason, especially for the sum they paid, which was pretty unheard of at the time for such a young company. YouTube's market share was an added bonus, but it was definitely not something Google couldn't beat given some time and the money they had.

But the fact that YouTube was the obvious target for all the litigations that were certain to come -- and outcome of which would also affect Google Videos and all other video streaming companies -- was a pretty big incentive for Google to get involved and make sure that they have a say in the control over the legal game.