I think he does actively involve himself in engineering-level discussions and decision-making, both at SpaceX and Tesla. Most CEOs don't do that, but some do – Bill Gates did that a lot when CEO of Microsoft – so it is not unprecedented. Designing something as complex as a car or a launch vehicle (or an operating system or an office suite) is a team effort, it is never going to be all on a single individual, and senior people are inevitably going to delegate a lot of the detailed analysis and design work to their subordinates – but a senior executive who actively involves themselves in engineering decisions can have a real impact on the outcome, for better or worse. He isn't formally trained as an engineer, but he has a degree in physics, and he is obviously a reasonably intelligent and very dedicated guy who has had years of access to some very experienced engineers, so the idea that he has learnt enough aerospace/automotive engineering to actually make a useful contribution as an engineering decision-maker isn't unbelievable.
I'm a bit of a SpaceX fan myself, but I feel like there is a big disconnect between what the average SpaceX fan actually believes about SpaceX, and the caricatures that many SpaceX/Musk critics like to paint. (Of course, there may be the occasional SpaceX fan who takes it way too far, and for whom these caricatures actually become true, but I don't think the vast majority of us are actually like that.)
A substantial portion of the Musk fanbase believe he's the one personally designing rockets and coding the software to land them.