The insurer will advise that you should not admit liability as it may prejudice their stance. Ultimately, the claim, and any claim made against you is your claim. If an incident was your fault, then you are not going to prejudice any claim against you by admitting to it. You have paid the insurer to indemnify you against any loss you may have incurred as a result of your negligence. Ultimately, fault can only be apportioned by the courts, but the court would frown upon someone or insurer who forced a case to go to court when it was clear from the onset they were liable. I would still advise everyone not to admit anything at the scene though, as it may provide an opportunity for your insurer to try and avoid the claim for some reason, and that is never wise.