[FeatureRush]

Most small and medium digital agencies I know of use the word "developer" in that way, as someone who sets up and manages CMS for clients, usually also doing customizations using stock plug-ins and sometimes writing plug-ins themselves. Handling all from configuration files, code to looks, UI and even marketing and photo editing when needed. And I can even tell you of some other companies that use title developer for people who only configure Microsoft Sharepoint for their clients, even more in my country people who sell newly build apartments are also called developers. It is just a word, it is not a real problem here.

The problem here in my opinion are your missed expectations and how are you reacting to this situation. I could just tell you "yes, those people don't know what a developer is" but that will not help you grow.

Looking at the whole thing from my perspective you seem to be very disappointed that this company did not meet your expectations and perhaps that you did not meet theirs. It's just a job interview. It's OK. Sorry if they were unpleasant, but it was their choice and arguing what a true "developer" really is will not change the outcome. I understand that you are upset, but what good will come from arguing about agency, that "doesn't even have..." ? There is not really a right and wrong in this situation, just you and that company did not fit together, do not think about it as your failure or as them abusing some kind of universal rule. It may hurt you, because you care, but really it's just a minor annoyance. A mismatch.