That's exactly what the Echo is.
The Echo allows the user to dive into the usee's memories, and experience them firsthand as though they were happening right before the user's eyes; and, to an extent, you can interact with that person's memories and manipulate them, and they WILL have an effect on that person. But the changes of a memory only effect that single person and nobody else.
The Echo isn't so much time travel as it is diving into a person's subconscious to view their memories in real-time.
