English Question

Hi, I started a thread three month ago, but I don't understand the final answer of it.
That was the question:
".........If you read this conversation:
Bryan: Is that an old photo of your friend?
Cathy: No.
Bryan: Okay, I always need to think about that person on the picture, who I thought was your friend. But they are not the same then.
Cathy (looks closer): No they aren't.

In this conversation Cathy's last statement "No they aren't." has the meaning:
"My friend and the person in that picture are two different people. They are not the same person.", correct?"


I was told by many users that this was correct, but the user cicerone imposter told me that I can't draw this conclusion. But I don't unterstand his explanation. Unfortunately he doesn't answer anymore. Can anyone of you help me to understand his explanation?
Link to the explanation: http://able2know.org/topic/308914-3#post-6130253