It is illegal in some U.S. States to charge more for a product or service if the buyer is using a credit card. Also, it is a violation of the merchant agreement with Visa, MasterCard, and American Express. This policy at Verizon is essentially a surcharge for payment via credit card. If one uses cash (cheque by mail, or ACH bank transfer), then there is no fee.
If one pays with credit card, then there is a "convenience fee" (surcharge). I suppose that their legal department could argue that they provide the Auto-Pay option for credit-card users to avoid the surcharge, but it remains debatable.
It certainly is not customer friendly. A more friendly way to cover their credit-card fees is to make the higher rate the standard price, and provide a discount for cash payments (cheques and ACH).
I took a fish head to the movies and I didn't have to pay. -- Fish Heads, Saturday Night Live, 1977.