If directly questioned, I would (and did) always answer honestly. I never lied to anyone, much less my children. If the incident was embarrassing or untoward I would keep the explanation brief along with the appropriate amount of regret.
This is not to say, that I feel the need to divulge - without specific questioning - everything about myself to anyone in earshot. Silence is, indeed, golden.
Perhaps more to the point, everyone, including a parent, has the right to say, "None of your business." There is no crime in keeping one's own counsel.