No, the guy who brought us the first private, manned space flight was Paul Allen, who funded the SpaceShipOne project. Burt Rutan and Scaled Composites actually designed and built the thing, along with the WhiteKnight launcher. On June 2, 2004, I was one of around 11,000 people who turned out to see test pilot Mike Melvill earn his astronaut wings (without an asterisk; he cleared 100km) at Mojave Spaceport. A truly extraordinary event.
I’m a big fan of Musk and SpaceX, but they had nothing to do with SS1.