If you watch any of the starbase videos (part 1: https://www.youtube.com/watch?v=t705r8ICkRw)

It's clear he knows a thing or two about rockets. Obv no single person is designing the thing, but it's clear he's highly involved.

I was going to link these videos too. Its evident he's closely involved with technical discussions and decisions.

I think he's more likely to be involved in relatively high-level (but still critically important) engineering decisions rather than "science". That distinction aside, I really wonder what makes people so sure he isn't involved, when every indication (interviews, etc.) is that he actually has a pretty good understanding of the principles SpaceX's rockets are built on, and the reasons they're designed the way they are.

Can you enlighten me? Why is this such a common refrain?

While he obviously isn't a real world Tony Stark, other people who were very definitely involved in the nitty gritty have said that he's involved in the design. While he likely isn't doing the simulations or directly working on the hardware, it's pretty obvious that he participates in the design at a high level at minimum https://twitter.com/lrocket/status/1512919230689148929

Like at any company, the people at the top aren't the ones who do the work. They need to have a broad understanding of the problem space, business opportunities, challenges and risk. They need to be able to understand what work is being done and understand the message that comes up to them. With that they can make high level decisions. From what I have seen, Musk deeply understands the problem space and can suggest engineers do low level stuff. I bet he suggests lots of stuff that the engineers go "erm no that is not possible". Those suggestions will never be seen by us. We will see the suggestions that happen like a rocket ship nose being changed by Musk.

If you don't think he's doing hardcore fundamental rocket design work at spacex, you've just been reading clickbait articles.