Can a braided fluvial create thick relatively continuous siltstone beds?
Braided channels are usually found in estuaries. Estuaries are usually on the coast. That being the case, it seems possible that now and again a high tide brought in some sand which covered the silt-filled channels, which then brought more silt, thus creating the layered structure you describe. If the site is now a long way from the coast, it doesn't follow that it always was.