I sent a support ticket asking the same question but also posing it here.
And yes, I know I'm probably the one person left in the US who doesn't own a cell phone.
Players who wish to use PayPal to charge up their Battle.net Balance or to “cash out” funds earned in the real-money auction house will be required to sign up for our SMS Protect authentication service in Battle.net. When you sign up for the Battle.net SMS Protect service, you will receive a text message on your mobile phone containing a code that you must enter on to verify your identity. Once verification is complete, you can then move forward with your transaction. After this initial verification, you will be prompted to enter a new SMS code from time to time when accessing a feature that uses PayPal. Note that standard SMS messaging rates apply -- check with your cell phone carrier for details.
Threats of violence. We take these seriously and will alert the proper authorities.
Posts containing personal information about other players. This includes physical addresses, e-mail addresses, phone numbers, and inappropriate photos and/or videos.
Harassing or discriminatory language. This will not be tolerated.