It depends on how you define "hurt"; while the CC company will take care of it, it's not instant - and it's no fun dealing with someone going over your credit limit on a cross-state shopping spree.
By all means, please - don't use debit cards online - but it's still not a panacea.
Also, sometimes charges are reversed via chargeback requests, and I have beaten chargeback requests because the customer claimed the CC was stolen, but I had the correct billing info.
By all means, please - don't use debit cards online - but it's still not a panacea.