It is true, we would not be able to talk about non-dual states without processing them through our thinking minds. In in so doing, we can mistake the actual experience for its interpretation. We make mouth sounds or write letters that are appropriate to our cultures. But it is an error to think that these concrete utterances and scribblings are the non-dual experience.
In short, the mind is what allows us to recall and interpret the non-dual experience. It accesses this state but it is not it. The non-dual field precedes the mind and everything else based on physical, material, structures.