Some years ago I had a native German explain to me that what JFK said really did mean "I'm a jelly donut," and he should have said "Ich bin Berliner." So YMMV.
Yes. And it's nice for a sterile Wikipedia page to offer the idea that there was only one way for JFK to say it, and that he did it correctly.
However! What I supplied was (one anecdote of) the reaction of a native German speaker who heard the line themselves. Their reaction was in line with the supposed myth. So no matter how smugly people today might denounce that as a myth, there were those in the intended audience whose reactions were exactly in line with the supposed myth. Which, of course, makes it not so much of a myth.