Musk absolutely should take credit for Tesla as it exists today.
The Tesla he bought into was just a research project. It was nowhere near the global brand it is today nor were they on a trajectory that would have put them anywhere close to where they are today. It was his vision that made it possible at all.
Similar to the founding story of McDonald's. Ray Croc bought the idea and made McDonald's what it is today. He didn't actually start the original 6 burger restaurants named McDonald's.
It's also questionable whether Tesla Motors would have had the same impact (or even survived) without Musk's efforts and leadership. They were making a very niche sports car at the time that was basically hand built. Musk is the one that got them to a mainstream commercial product.
Fine, but when do we stop assigning money and drivers as co-founders? You can look at situation like Lee Iacocca did the same thing for Chrysler, but he wasn't labeled as a co-founder.
But he very much did build SpaceX from nothing (well, his Paypal money), and his unconventional approach is responsible for their success.