On a narrow road it is always hard to prove, unless you have it on a dashcam. Contact your insurer and advise them that you are in no way liable for the incident and that you expect them to fully reclaim your lawful entitlement. Do you have photos of the scene, the time and the damage on both vehicles? If you do not, then any attempt to find the other party liable is most likely to fail. Get your insurer to contact the other insurer and advise that they find them wholly liable. Ask them to provide evidence to substantiate why they feel different.