Well, I'd be very interested to see how ICANN could get post offices, like the United States Postal Service or Royal Mail, to go along with submitting to ICANN accreditation. That aside, data on people who own USPS-provided post office boxes and boxes held at commercial mail receiving agencies (CMRAs, like the UPS Store, and so on) can be obtained from the USPS, per 39 CFR 265.6(d)(5)(i) through (iii):
(i) To a federal, state or local government agency upon prior written certification that the information is required for the performance of its duties.
(ii) To a person empowered by law to serve legal process, or the attorney for a party in whose behalf service will be made, or a party who is acting pro se, upon receipt of written information that specifically includes all of the following: (a bunch of things)
(iii) In compliance with a subpoena or court order, except that change of address or boxholder information which is not otherwise subject to disclosure under these regulations may be disclosed only pursuant to a court order.