A credit card the account is with visa, tho it may be managed by your bank thanks to partnerships and bank end integration. Depending on the circumstances you actually will be directed by your bank to contact visa or who ever directly or be forwarded by your bank.

Do you have a source on this? Because it directly contradicts EVERYTHING I have ever experienced. Visa is a payment processor, but more as a middleman. I've even been redirected (through automated systems) back to my bank when making a purchase using a Visa card. Any disputes are handled by bank. You can't get a Visa card without going through a bank. My debit card has a MC logo and can be used as such, but it's also my ATM card.

Your point about debit vs credit is valid, though possibly more convoluted than needed. On credit, it's someone else's money in limbo, until the bill is paid.