No, that's not accurate. His stockholders and/or venture capitalists do the funding -- remember that "funding" means answering a relatively simple question about risk versus reward. Someone still has to manage projects, make technical decisions. That's what Musk does.

Consider a parallel example -- Steve Jobs and Mike Markkula. Jobs made product decisions, Markkula funded them.

You are mistaking (part of) the startup world with how the real world works at large. (And to be clear, I'm not pretending that Elon has not made any direct technical decision; that, I don't know)

So that you get a sense of what can happen in the wild world, let me copy past wikipedia for you: "As of May 2012, SpaceX has operated on total funding of approximately $1 billion in its first ten years of operation. Of this, private equity provided about $200M, with Musk investing approximately $100M and other investors having put in about $100M (Founders Fund, Draper Fisher Jurvetson, ...)."