They also had the connections to turn around and sell it to someone who could anchor it against the legal challenges that everyone involved knew it would have to face. Streaming video had been done before, but Youtube was the first place where you could upload your own video and show it to others without having it be manually approved by the site operator.
Given the current state of copyright law it was pretty much insane for them to expect to be anything other than a lawsuit magnet; unless they had a plan to deal with it.
Or, just as likely, on the other side of the spectrum, they tried to create the best site they could and got multiple offers on a daily basis since inception.
In other words, just because they sold to Google, doesn't mean other companies didn't also offer money that would have made the founders millionaires multiple times over if they had accepted any buyout offer in the previous 6 months to a year before that. Most any startup that sells for millions or billions of dollars didn't just accept the first buyout offer they got and it happened to be for a lot of money; no, they had been negotiating and evaluating serious offers from day one, all the while improving their software for months or years.
Given the current state of copyright law it was pretty much insane for them to expect to be anything other than a lawsuit magnet; unless they had a plan to deal with it.