who's at fault?

A few months ago, I was involved in a car accident on a mini island. The point of impact on my car was passenger side wing and on their car I it was driver’s side wing. At the time of the accident the other driver admitted to being at fault and offered a cash amount to settle without involving insurances companies, something I wasnt willing to do. However, my insurance company have now got cogent law involved and they are saying I should take 50/50 liability because the other side will argue they were on the island first, which is complete B/S. I just wanted advice from a naturals point of view?
Thanks