Let's put it this way - if it wasn't for private entrepreneurship and Musk's vision, SpaceX wouldn't be here no matter what DARPA or NASA would have done.
Elon's leadership drive and capital had the catalyzing effect. Without Elon, all the capital in the world would've gone into laggy bureaucratic procurement and project management pie in the sky bridges to nowhere. ARPA might've done what today's DARPA/NASA does not do.
Let's put it this way - if it wasn't for private entrepreneurship and Musk's vision, SpaceX wouldn't be here no matter what DARPA or NASA would have done.