AVS doesn't deny anything. Its a status code returned on the auth. Its up to the merchant to reverse the auth if AVS data shows it doesn't match(Exact Address,Zip Code, CVV) or send the auth off for settlement. Merchant has almost no recourse if transaction is marked as fraud and the AVS doesn't match.
It may be up to the merchant, technically, but in reality systems such as Authorize.Net allow you to configure it at the gateway to reject transactions based on various AVS criteria. Many of my clients also only allow shipping to the AVS verified billing address as a way to weed out much of the fraud. For many products, only allowing shipping to the billing address is a reasonable restriction.
