By default, the billing address fields are always required to the customer from the main event listing website. You have the option to disable the billing address fields in your Account Settings under the "Checkout" tab. Change the option from "Show" to "Hide" the billing address to completely remove those fields so that your customers don't have to fill it in.
When logged in as a ThunderTix user, there are no fields that are required. All billing information can be completely bypassed to make order processing faster.