Uh yes, we do. It works in precisely the same way that you can walk from "here" to "there" by taking a step towards "there", and then repeating. The cognitive dissonance comes when we conflate this way of "having a conversation" (two people converse) and assume that the fact that they produce similar outputs means that they must be "doing the same thing" and it's hard to see how LLMs could be doing this.
Sometimes things seems unbelievable simply because they aren't true.