The term of art for dating based on soil layers is called stratigraphy, and doesn’t necessarily require radiocarbon dating. E.g. if you find a layer of silty sediment with clamshells widely dispersed, on a site you know was a lakebed that dried up >100 kya, it’s probably a safe assumption that the layer you’re digging is at least that old.
Sediments are absolutely shifted over time as you suggest, but what matters is the relative positioning of the layers, not their absolute thickness, and it’s generally pretty easy to spot when layers have been disturbed by human or geological activity.
I wasn’t able to get my hands on the original journal article from Nature to see exactly what techniques were used on this particular site, but a detailed description of the stratigraphy is generally included in any standard dig report.
What kind of radiometric dating is used for sediment? Is it not possible for older sediment to shift around and cover newer stuff?