The flaw in your logic is that the stock is not made of soil. While compressible, it is not that compressible. Go back to your Strengths of Materials text and review point loads versus distributed loads. Can have both, sometimes at the same time. Some particular materials may not embrace one or the other, but both are viable loadings in metals.
The purpose of the bottom metal, as with regard to the action screws, is to act as a washer of sorts. To be an area larger than the OD of the pillar so that it can not easily be pulled thru the stock. Even single shot target actions use what amounts to being a large washer under the screw head. We call it an "escutcheon", but it is just a fancy washer.
If the action is moving on the pillars either someone didn't torque the action screws, someone did a bad bedding job, or the stock is so flexible that it wasn't worth the effort and should have been tossed.