It doesn't actually have memory in that sense. It can only remember things that are in the training data and within its limited context (4-32k tokens, depending on model). But when you send a message, ChatGPT does a semantic search of everything in the conversation and tries to fit the relevant parts inside the context, if there's room.

All of these LLMs should have walls between individual users, though, so that the chat history of one user is never accessible to any other user. Applying some kind of restriction to the LLM training and how chats are used is a conversation we can have, but the article and the example given is a much, much simpler problem that a user checking his own chat history was able to see other user's chats.