This is not how it works in Europe or in the US. The chargeback occurs through the payment processor, and both the merchant and the bank issuing cards with Visa logos are customers of Visa using their payment network to manage charges. When your bank issues the chargeback on your behalf, they are doing so through Visa's systems.
If those obligations are by law in your jurisdiction, than you are probably covered. In jurisdictions where that is not the case, the bank is bound by Visa's policies if they want to issue Visa logoed cards. That's why this is such a far-reaching and problematic development.
