Subscribe to ChatGPT Plus and you get GPT-4 access. I tested your scene with it, its response:

In the above scene, Joseph determined that Allie's parents were dead by testing the bad guy's knowledge of Allie's upbringing. He pretended to be Allie and sent a text with false information, saying she grew up in L.A. instead of New York. When the bad guy, pretending to be Allie's parents, responded by confirming the false information about growing up in L.A., Joseph deduced that they were not her real parents and concluded that her parents must be dead.

edit: though I think the "your parents are dead" bit might still enable it to make the connection to Terminator.