If you have a dispute with the merchant the credit card company (or your bank with a debit card) may ask you to first try to resolve the issue with the merchant.
But if you're not the one who used the card, if it was used by a thief, and you have no business relationship with the merchant, I don't think they can ask you to deal with the merchant. I mean, in this case the merchant was in India.
Even if it's the company across the street, if you didn't order anything then it's the bank's problem.
But I strongly prefer a credit card-- if there's a problem they gotta get money from me. With a debit card they drain your account and you've gotta fight the bank to get your money back.