I'm a non-native speaker. When I was a student of English my teachers mentioned this answer was to be avoided in formal situations, except for its literal meaning. Years later I heard it twice, as a reply to questions, in formal lectures at my professional congresses. What I want to know is whether it is proper to answer that way, when you me an "I don't know" or "I have no idea", in formal spoken or written English.
The Chief of Detectives in a major city's police force is at a press conference, reporting on progress solving several mysterious disappearances of prominent people. Minutes earlier, the CoD and his detectives have bemoaned among themselves that they don't have a clue. According to your English teacher, the CoD can say, in the press conference, that he doesn't have a clue. But does he say that? Of course not!
A person whose opinion counts for something can use the phrase "don't have a clue" only when it is safe -- for example, when she is among peers who are also friends, none of whom are likely to stab her in the back later.
As for the International Congress where you heard the phrase: if it was in a formal presentation, I'll bet that it was about an aspect of the subject in which everyone would agree that no one had a clue or it was a dismissive answer to a question the answerer regarded as stupid.
MDs should be especially wary of using the phrase if a hypochondriac could be anywhere within earshot.
In situations where nothing is at stake, "I don't have a clue" is OK. Such situations are unlikely to be formal.
In most spoken language, as you've noticed, it will be quite acceptable, except probably in technical settings. However for written language, it's only really acceptable in informal situations.
For example, in a story, a tweet, or blog post, no matter the audience, it would be acceptable, but in a formal letter, technical paper, or legal document it would not be acceptable.