I think using the word "conflict" is idiotic, but it helps to rephrase it. Because indeed, like you, I've never in my life had "conflict" with anyone in a work setting, I've had plenty of disagreements though and that's just part of the job/life.
I tend to just make something up here on the spot honestly, because as you said, I'm not keeping a book of grudges where I record every single disagreement I have with a colleague. I'll say something like "On Project X (which I've been talking about during the interview) we had a disagreement on how to do Y. I resolved this by gathering the facts on the pros and cons of method FOO vs method BAR, and we sat down as a team and discussed the approach we preferred to take". The anecdote is usually completely made up, but there's been enough situations during my career where the approach has definitely made sense.