Content-Type: text/html
The phrase can be interpreted in two ways:
Going by strict grammatical rules, technically the "ein" is wrong unless the oneness is being emphasized. However, this is one of not so useful rules, which should include a "Usually...". It is not a rule well known or used in German everyday language.
The best parallel in English would be "I am a Frankfurter" which of course also means "I am a sausage". Although the sentence is grammatically correct you would normally disambiguate by saying "I am from Frankfurt". In German you could disambiguate by leaving out the "ein".
The context made it very clear, though, so nobody misunderstood JFK when he delivered his speech. Everybody listening to it understood it to mean that JFK was just one of all the Berliners.
Contrary to public belief, there was not a roar of laughter when JFK delivered its speech. Recordings instead show applause.