I take your point that credit card numbers can be compromised off-line as well as online.

What's different about online credit card crime? A number of things:

a) volume, steal 100 or 10K numbers in a single swoop. Drop a latte-sized randomized charge on each one.
b) Inclusion of additional info. When I use plastic in a cafe, I don't give them my address/phone/email. Often this is included in an online transaction.

Just so we all don't panic and chop up on the plastic right now, keep in mind that you can disavow any charges you did not make, or that have not be satisfactorially fulfilled. It is the responsibility of the vendor to prove that you did make the charge and that the service has been fulfilled. Until then, you don't pay. This can come in handy when you are not satisfied with the goods ( and yes this is a legal and ethical use of this feature of plastic).