That's entirely up to you. I will tell you that while there are states where an employee has the guaranteed right to place a rebuttal in their personnel file if there is anything with which he does not agree, Missouri is not one of those states.

I do not know your boss or your company culture. You're the only one who can judge if it will help you or hurt you. All I can tell you is that in your state (and in most others) your employer has no legal obligation to take notice of any rebuttal you make. Whether yours will or not, and if so, whether it will help or hurt you, is not a judgement we can make from here.