Yes, they can, since the insurer's own internal decision as to fault, responsibility, etc. is not a binding legal determination and is not enforceable; they are allowed to revisit or change it. Since you write that you had only third-party liability insurance, presumably you are taking about the decision of the other driver's insurer. That means that if you disagree and feel their driver was at fault, the only way to seek compensation (e.g. repair costs) would be to sue their driver in court and prove that he or she was at fault (you sue the driver, not the insurer).