Nope, you're not missing anything. Startup teams are so small that everyone on the team has to be able to add value by creating something tangible. There's no room for middle-management.
And "non-technical" doesn't mean "middle management". Or, more to the point of the OP, there doesn't seem to be room for anyone who's not a programmer. That's a lot of roles, IMO. (Case in point, I have a CS degree and extensive business experience and have no desire to be a "programmer.")
Agree. Top-management takes care of business development while the tech team develops the product per se. Anything added to the middle would be considered fat to a lean agile body.
Tangible things are not the only way to add value to a start up. Popular start up methodologies, and I speak specifically of Lean Start Up and Customer Development, all have a strong focus on making sure you're building a minimum viable business, not just a minimum viable product.
However, the statistics are such that it's rare to have a start up team with the self-awareness to recognize this need connect with a non-technical person capable of satisfying it.