Ron Kritzman wrote in "Clueless Hollywood":
Verizon and other ILECs have their own payphone subsidiaries which have been placing private (COCOT) payphones in locations outside of their basic ILEC territory (in addition to their own ratecenters and territory) for several years now.
Verizon private payphones are located in BellSouth territory as well, so it's not unusual for Verizon branded private payhones to be located in SBC (at&t) Ameritech territory as well.
Qwest (US West) has private payphones in states and locations outside of Qwest (US West) ILEC territory, including in BellSouth states.
Sprint (United and Centel) has placed Nortel Millennium payphones in most Greyhound Bus Stations in the US, for several years now, regardless of who the incumbent local telco for that city happens to be. Over the past few months, these payphones are being rebranded as Embarq, since Sprint-Nextel has begun to spin-off their legacy United and Centel ILECs into the now-separate Embarq company. This apparantly includes payphones which were once branded as Sprint.
I don't know if at&t (SBC, Pacific Bell, Ameritech, and SNET in Connecticut) has private payphones outside of their territory (i.e., in non-at&t ILEC ratecenters in at&t ILEC states; or in Qwest or BellSouth or Verizon or Cincinnati Bell locations).
BellSouth got out of the payphone business, at least in BellSouth states, a few years ago. I don't know if BellSouth ever owned BellSouth branded private payphones in other states though. But with the "new at&t" (SBC, Ameritech, SNET) soon to takeover BellSouth, I wonder if "at&t" branded payphones will soon be seen in the southeast!