Is it bad not to answer this question? In other words, should I have been not honest and make up a story?
There is a third option in this kind of situation: take your best guess at the purpose of the question, and then offer them some other way to get the information they're after.
In this case, the purpose of the question is most likely to explore whether you're capable of communicating and resolving such conflicts in a productive manner. So one could instead offer something like this:
"I've actually been really fortunate with my supervisor/s and we haven't had any significant conflict, but perhaps I could tell you about a conflict I had with one of my course coordinators, if that would be relevant here?"
(Or anybody else who you've had a conflict with, but the more similar to a supervisor/supervisee relationship the better.)
If that's not what they're looking for, they can clarify what the point of the question is, but this kind of approach shows a willingness on your part to work with them.
Footnote: while each question in an interview might be there for a different purpose, every question is also a de facto test of communication skills and collaboration style.
If I have to choose between working with the candidate who says "I couldn't do the thing you asked me to do, so I did nothing", and the one who says "I couldn't do the thing you asked, so I thought about what the next best thing would be, and did that instead"... I probably want to work with the latter.
Footnote #2: since none of us are perfect at divining the intent of such questions, especially in the pressure of an interview, it is important to phrase this as an offer (note the "if that would be relevant?") rather than assuming this is the correct interpretation and going straight on to answer one's own version of the question.