A few years ago, I worked as an administrative assistant for an attorney. She was a little bit paranoid when it came to the Internet. Her fear of things such as identity theft caused her to tell me that she'd never buy anything online.
Thankfully, those who feel the way that she felt have other options when purchasing things from merchants who have accounts with PayPal. PayPal's new Virtual Terminal feature allows one to accept credit card or debit card payments via phone, fax, "post" (mail) or face-to-face transactions. That way, customers don't even need to have the ability to access the Internet.
Of course, anyone who knows anything about the modern world of finance knows that personally abstaining from e-commerce transactions doesn't guarantee that one's financial information won't be floating around in cyberspace. Most banks these days conduct business via the Internet. Merely having a bank account can make one vulnerable. Unless one is a total Luddite who buries one's money in a tin can in the back yard, and who never uses credit cards or debit cards, it's delusional to think that avoidance of e-commerce transactions offers any ironclad guarantees.
Consequently, my personal opinion is that one might just as well join the 21st Century and take advantage of the ability to buy things online, taking care to exercise reasonable caution when doing so. (For example, it's generally better, when buying things online, to check to make sure that there is real-world contact information for the seller, so that it's easier to prosecute the offender if a fraudulent transaction should take place.)
Even so, it's great that PayPal now enables one to offer other options to customers who want to pay with credit cards or debit cards. It isn't hard to think of situations where that could make the difference between making the sale or not making the sale.