Funny how in an article about common misconceptions a myth like that gets to live on (by being replaced with a new one).. I can't speak for Berlinerisch, as I've never lived in Berlin myself, but in standard German both versions - with and without the indefinite article - are 100% correct. The version suggested in the article might be slightly more common ("Ich bin Berliner"), but for JFK's speech I'd even go as far and say his version was better, simply because it stresses that he's "ein Berliner", just like all the other people listening to his speech. As I said, though, both versions are correct, and neither of them sounds better/worse. (Sorry, no source, but I know a bit of German.)