got a claim letter from other persons insurance

i got into an accident on june, me and the guy settled on outta pocket and we both left. we kept in touch but went dead on me the beginning of august. i received a letter from his AAA insurance asking from a exchange of insurance but at the bottom it reads “please return this to my attention in the envelope provided. if we do not hear from you within 15 days, we will process our insurers claim for payment directly with you”. so my question is can i wait till i get that direct payment option. i have 2 days left since i barely got the letter today at the mail and i have no adjuster or anything(i have insurance but dont want rates to go up). do you guys recommend waiting it out, since i do wanna pay outta pocket. i even asked the guy for a quote when he went to the shop but he never gave me anything. which to me sounds like he wanted to be slick and file a claim down the line. it’s been 2 months since the accident and he’s barely filing a claim. if i got a quote from him it’ll be much easier for both of us but it seems like he wants to go through the insurance