I too was puzzled and annoyed after attempting to pick up messages from home on private pay phones ("Those New Private Pay Phones: Some Won't Get the Messages" by Beverly Beyette, Nov. 10).
I devised a simple solution, however: I dial my home number. When the phone begins to ring, I press one or two numbers. (This does not interfere with the ongoing process.) If I hear a tone when pressing a number, I am fairly certain I can retrieve my messages. If I do not hear a tone when I press, I hang up and, because no one answered, my money is refunded and I go elsewhere.
I seem able to retrieve on some phones that are private, yet not on others.