“Nothin’ But A Hound Dog” was not, in fact, written by Elvis Presley. Windows 95 was not, in fact, programmed by Bill Gates.

No, this is entirely correct.

You have to look at things at the right level of abstraction.

Bosses "program" people, they set them to work on things that need doing. They can be more or less involved in the actual process, but ultimately they're responsible for delivering the thing.

Developers write all the code. Some may feel that they built the whole thing (I have been that person) but that neglects the role others play in figuring out what needs building and actually making it happen.

Edit: I don't believe it's right for others to take credit for someone else's work. I just think that when an executive hears a boss "built" something, they don't think "wow, what an amazing coder". They don't think about code at all. This person delivered a thing that was built. They built it in the organization. That's all it means.