When you become a member of Americas Mailbox,you will be given a legal address that is good for all purposes, including being on your driver's license.
What you may run across with some credit cards (and also banks and brokerage firms) is this part of the Patriot Act:
CIP (Customer Identification Program) rule (31 C.F.R. 103.121 (http://www.gpo.gov/fdsys/pkg/CFR-2010-title31-vol1/pdf/CFR-2010-title31-vol1-sec103-121.pdf)), which is the regulation implementing Section 326 of the USAPATRIOT Act that requires a financial institution to get the following customer information (bottom of page 480 from PDF above):
(1) Name;(2) Date of birth, for an individual;
(3) Address, which shall be:
(i) For an individual, a residential or business street address;
(ii) For an individual who does not have a residential or business street address, an Army Post Office (APO) or Fleet Post Office (FPO) box number, or the residential or business street address of next of kin or of another contact individual
All PMB addresses in the country have been flagged as non-residential for purposes of this program.
However, you simply give them the "sticks and bricks" street address of any friend, relative or contact individual of your choice and you will have no more problems. You must STRESS that YOUR mailing address at Americas Mailbox is the ONLY way to contact you. No mail or correspondence will ever be sent to your contact individual.