I think it is too confrontational for a goodwill later. You'll need a healthy smattering of honey if you want to sway them to your side.
Perhaps you could say something like:
"Thank you for taking the time to reply to my initial letter. I would like to take the opportunity to reiterate that I am not disputing that my payments were late. I am asking for forgiveness, and a goodwill adjustment to remove the lates reported to the credit bureaus. I take my financial obligations seriously, as I realize how important good credit is. I would never intentionally pay late, however <insert banking error situation>. I have done <insert plan of action> to make certain that this situation never happens again.
You stated that “Accredited is obligated to report accurate information regarding the status of your loan while you are a customer of ours.” I agree. Because you have the ability to forgive mistakes, and rehabilitate accounts at your discretion, I'm requesting your consideration to forgive and remove the late payments. I sincerely appreciate your assistance in this matter."
If at first you don't succeed, try & try again. Just use a little more honey each time. Eventuall (hopefully), they'll get a tummy ache and cave to your will. 