A company is more than its most visible members. There were likely plenty of competent people in the hierarchy that were there before Musk and were able to continue that trend of competency until Musk decided he needed to control more and more of the intricacies of the company.
The difference isnt what he was doing before to make things run smoothly so much as what he wasn't... that being getting in the way. He was a glorified PR guy. Which he was great at. Running a tech and manufacturing company? Not so much.