Shotwell doesn't "run" it. She is president and COO, sure. The vision, strategy and engineering is all Musk. Read the book Liftoff. Musk doesn't get much credit for his engineering work and often gets written off as just "investor" type.
Musk is not a rocket scientist.
I'm quite sure that Musk understands the engineering totally and makes important contributions. Plus, his instincts in providing direction as a CEO are excellent. Very few CEOs understand tech like Musk does.