Public liability insurance covers the loss someone else has suffered that you’re responsible for. But, it will only cover the actual value of the damaged item, not the cost to replace it with a new one. That can leave a gap between what you’re liable for and what the policy covers. That’s why it’s best for these claims to first be made on the building or contents insurance, as those policies pay replacement value. That insurer will then seek to recover their loss (the full replacement value) from you and your liability insurance will cover this whole amount (since that is the amount of the loss the insurer has suffered). The homeowner’s excess will be covered too and they won’t have an adverse claim history either, since their insurer was fully reimbursed for the claim.