Do that in Javascript. Or HTML. Or CSS. Or by that logic is a web developer not a programmer? What about microcontroller programmers?

I could easily write a full logic program in SQL where the API just feeds it data, which is the inverse of how you treat SQL. Admittedly that's not as common, but it happens pretty frequently in areas of big data, like medical.

I've hired Senior Software Engineers that were DBAs, and others that weren't. They were a development team, all programmers in their own right.