Musk's argument is more that cameras should be sufficient because humans can drive using only two eyes to perceive the driving environment. He always neglects to mention that humans do this with a combination of sight and a brain capable of general intelligence. I'm sure it's true that if Tesla invents AGI, self-driving with just cameras will become tractable. But "real hard problem to solve" doesn't begin to capture the difficulty.
In reality, since no one has yet invented a self-driving computer, it's impossible to say what components are necessary or even whether there may be more than one way to skin the cat. But one source we should probably take with a grain of salt on this issue is those (like Musk) with an intense commercial interest in one perspective.