Idiomatically, when one says he is from Berlin, he says, “Ich bin Berliner.” To say that you are an American you would say “Ich bin Amerikaner.” Berliner or Amerikaner can be either a noun or an adjective, you figure it out from context. I like to make an analogy to the expressions “I’m Danish” and “I’m a Danish” spoken in English, but the case isn’t quite as strong. “Ich bin ein Berliner.” is grammatically ambiguous, but idomatically it sounds like he said, “I’m a Danish.”
I’m sorry, my German I teacher, a lady from Salzburg, said that Kennedy said, “I’m a donut.” She didn’t need a lot of ‘splaining. If you want to say you are a resident of Berlin, you say, “Ich bin Berliner.”, regardless of your accent.
Ah. JFK may NOT have said, “I am a Jelly Donut” in German, But Jimmuh Carter once said “I have Always Lusted after the Polish people” in Polish. LOL. I remember it! It was particularly funny in light of his Playboy interview where he admitted to “Lust in his heart”