NEAL! What is happening to my posts? I posted a detailed reply to this earlier and poof! It’s no where to be found!
Are you sure you really posted it, Steven? Don't get me wrong, I'm just trying to make sure, because this is potentially quite worrying, you know.
Duden might say that the indefinite article is “often” omitted with certain nouns, but that was not what I was taught in the 70s and 80s. I was taught it was always omitted with certain nouns and it is not optional to omit it. And, I’ve never heard anyone use an indefinite article not followed by an adjective before those certain sorts of nouns, either in writing or in speech. Not once. The rule is if the noun is not preceded by an adjective, the indefinite article ein or eine is omitted as long as the noun refers to origin, profession, an official position, a worldview, a religion, or a social status. Then examples are given. That’s what I learned and all I’ve ever heard when native speakers speak and I’ve never seen it written otherwise, ever.
You won't get any argument from me, Steven. I definitely agree with you more than with Mr. Duden's heirs in this instance - if anybody said something like "Ich bin ein Professor" to me, I'd conclude they either weren't a German native speaker or quite urgently needed their head examined.
But as it was, everybody just appreciated the sentiment, I think - it wouldn't have occurred to anybody to start quibbling about whether or not the indefinite article was surplus to requirements.

On the other hand, you know, after I'd posted my - perhaps unnecessarily flippant - comment, it did cross my mind that it was probably quite fortunate Khrushchev hadn't decided to wall off Vienna instead. 
Thank you Alharacas,
Yes, this is what I always thought. Obviously no one would have been confused about what JFK meant with his “Ich bin ein Berliner” comment because the sense that he was expressing solidarity was clear. But, that doesn’t make it especially good grammar.
I enjoyed Jerry’s Huffington Post article wherein the German linguistics professor in Berlin is cited saying that the language JFK used was “grammatically absolutely acceptable.” Ah, it’s hard to argue with someone credentialed like that, but that is certainly NOT what I was taught, and it is not what I experienced. Quite the contrary. I had it drilled into my head 40 years ago that you never use the indefinite article ein/eine with certain nouns that designate, a fundamental characteristic of a person, specifically those having to do with ethnicity, citizenship, profession, religion, social status, place of origin, sort of the group a person might belong to, unless an adjective is placed between the indefinite article and the noun. On the contrary, you have to use the indefinite article with some nouns describing people. When you are talking in generalities about a person that don’t go to fundamental characteristics, then it’s different, like saying “Er ist ein Idiot.” That’s where German can be tricky and knowing these small nuances really matters.
This is why when I heard JFK say “Ich bin ein Berliner” an alarm bell went off in my head with a flashing red light, saying WRONG!! But, in this case perhaps it was the translator just taking a sort of poetic license of sorts. He couldn’t obviously have had JFK say “Ich bin Berliner” because JFK wasn’t a resident of Berlin or from there, so that would never have worked. The alternative of using ein to communicate a sense of solidarity, although being an outsider is interesting, but I’ve never heard anything like that before, and I would suspect the vast majority of native German speakers haven’t either. And, how many would really use this very rare nuanced use of ein in this way ? Probably no one.
I have that 2009 version of Duden Grammatik, 8.Auflage, pps. 331-332 where they say the indefinite article is “often” omitted. My experience is that it is always omitted with certain nouns.
But, then Duden Grammatik really gets into some advanced detail that most people just aren’t going to learn in most language schools.