Not surprised that banks recommend using a credit card, because of course they are hoping you don't pay it off every month and they can make $$$$ on the interest. For debit cards they only get the transaction fees, and potentially an annual fee from you, so why would they recommend that?
I've had a credit card number stolen twice, never my debit card numbers - which I use nearly all the time because then the transaction is paid and I don't have to worry about remembering to pay the credit card before the interest kicks in. I use credit cards mostly for online shopping and travel.
Agree with those who say best thing is to keep an eye on your balances and jump on it immediately if there's anything weird. If you're worried, ask in advance what your financial institutions policies are, how they monitor for unusual activity, and who absorbs it when your card number is stolen. In my experience, larger institutions are quite good about it.