Maybe I don't understand what you mean by "perfectly rational". I'm using the definition from the article: A perfectly calibrated individual will be right X% of the time about statements in which they are X% confident.
A perfectly rational person would have all available information. Since ducking wastes energy vs. doing nothing, if they were going to get hit they would duck, and if not, they would do nothing.
But again, being perfectly rational is impossible.
Are you using a different definition?