It's not a really a "myth". Both have zero or a small amount of fraud liability (i.e., they give you back all of the money, or all but say $50 of the fraud). But! If you have fraudulent activity on a credit card, you're out that much credit until they remove the charges. If they do that much fraud on a debit card, you're out that much cash out of your checking/savings account until they credit your account back.
I'd much rather have one of my credit cards less usable for a day or two than have the account I use to pay a lot of bills from drained for a day or two
I'd much rather have one of my credit cards less usable for a day or two than have the account I use to pay a lot of bills from drained for a day or two