The big Target scam hit people in their own hometowns, not while they were traveling. And, it hit everyone. Not just certain banks. No bank can fully protect your account from scammers.
Debit cards do not offer quite the same protection as credit cards, even when they are backed by VISA or Mastercard. When shopping online especially, use a credit card. If you're traveling and using a debit card, alert your bank before you go. Quite often, Transaction Review Departments will block a debit card when it's being used out of town because they think it's fraud.
P.S. We see MORE fraud from debit cards used in Wal-Mart stores than anywhere else!!!