Most hedge funds in fact DON'T beat the market though. In almost every case you would have been better to buy index funds and hold versus put your money in a hedge fund.
Correct. The true function of a hedge fund is not to beat the market over the long haul, which is generally impossible. The goal is to avoid losing huge amounts of wealth, for people who have way more money than they need. Hence the name --- you put money in there as a hedge against short term losses in equities.