What does "counter" refer to in "countersink"?

(Non-english questioner) To countersink means to drill a sloped hole so that screw heads can sink into the material to be hidden.

In German for example the term for this action is "senken", which would translate to only "sink" (not "countersink", which would literally translate to German "gegensenken" - which doesn't make any sense in German).

I know the followng meanings of "counter":

• a "mechanism" to increase numbers
• something like "opposite" or "reverse" (like in "counterattack")
• the furniture in a shop or bar where the salesperson works

None of them makes sense for screws. What exactly does "counter" mean here?

The conjecture on this in the OED says

Etymology: counter- prefix, apparently in a sense akin to 8 b, the hole being the counterpart of that which is to be sunk in it.

My grandfather was a blacksmith (now long dead). My understanding is that a countersink (also called a bob-punch), is used to form a depression in the surface of plates to be joined together when rivetting. Without this, the head of the rivet projects entirely and is subject to damage. If the head is broken off, the rivet will sink into the plate. The indentation counters any tendency to sink. I suspect the term also applies to indentations for horseshoe nails.

Unfortunately my grandfather and my father are deceased and I can't find anything online to support what I'm saying.

I'll leave this here for now and see if I can find anything further.