You need to clear a lot of snow before you can stand on the ice that you're drilling in (You can't drill straight if your rig's sitting on snow, you need to dig until you hit solid ground, and in this case the ground is ice). That's the "boots on the ground" part. They were physically there to do the drilling (as opposed to giant automated core drillers such as DISC[1], which don't require "boots on the ground" so much as they just require one or more operators to oversee operation)

The ancient mud's from hauling up the ice cores, not from standing 3 kilometers deep in a giant hole.

[1] https://icedrill.org/equipment/deep-ice-sheet-coring-drill