Striking Vehicle Denying Liability (Motor Vehicle Collision). Philadelphia, PA

Good evening to the legal minds of Reddit,

I was involved in a motor vehicle collision while crossing an intersection. I was struck in the front driver side by a vehicle blowing a red light. Unfortunately all those present to witness the incident ran from the scene and Philadelphia Police were unable to come to document the accident due to extremely high call volume. The striking vehicle's driver requested that I allow him to see an estimate prior to him putting a claim in with his insurance company. I have all the correspondence via text message. I informed him of the cost of the damages and he reported to me that it would "have to go through insurance." During our conversation I stated to him that I doubt he would like to pay that out of pocket to which he stated "Yeah, I was thinking if it was under a grand, but that's definitely what insurance is for." Although all of this information was provided to his insurance company I was informed that the driver "disputed his liability" and that "the text messages aren't enough to overturn the decision to deny the claim."

My questions to you are:

1.) Do I have any legal ability to have this decision overturned?
2.) Would this be an insurance law or personal property case?

Any information that you can provide would be extremely helpful. I truly appreciate all of you attorneys that donate your time to us redditors.