Auto insurance trying to back charge me for adding a driver to policy

Ok so this will be a little long.

I recently bought a vehicle in August and got insurance same day (I am recent graduate so I haven’t had a car or auto insurance for a few years).

While on the phone getting the insurance, I told them to exclude my boyfriend from the policy. We are in Massachusetts, so he needs to be excluded if he will not be on the policy and lives with me.

They created a policy that had him excluded. This was August 6th. The same day, I believe, they sent me a document for him to sign to keep him excluded. I say “I believe” because I don’t remember seeing this form until August 28th when they sent an email about it. But, the email doesn’t specify what document is outstanding, it only says a document needs to be signed.

They had a deadline on the app for September 15th to send it in, or my policy premium may change. I sent it in September 6th.

They are now trying to back charge me from August 6 – September 6, saying he was added onto the policy since I did not sign the form until September 6th.

Massachusetts law allows insurance companies to add drivers in the household to the policy is they “reasonably believe” they are driving the vehicle. I heavily disputed this charge with customer service, stating that THEY gave me a deadline of September 15. I adhered to that deadline. Regardless of that, there is no realm they could argue they had “reasonable belief” that my boyfriend was a driver from the same day my policy started until I submitted the letter. I created the policy with him as excluded, and expressly told them he is excluded. Customer service said there is nothing they can do. I am cancelling the policy, but payment for the back dated charge is still due October 6th.

So my question is, how can I go about disputing this further? If there any merit in disputing it? If I refuse to pay, will that hurt my credit?

Thank you!!