The dominant factor on this scale is the strong nuclear force, which governs interactions at the scale of quarks - much smaller than molecules.
In the sense that it did not become 0.952 meters long. It didn't "become" anything - it did not change at all. The universe grew around it, or perhaps "underneath" it. More space appeared for it to exist in. It's like putting an iron rod in a 10 meter square house, then moving the walls out another meter.
Edit: let me phrase this another way. Let's imagine that you and I were pulling on the bar at either end. We could pull it forever and ever and it would never come apart (unless it rusted and became brittle or something, but let's imagine it doesn't). That's because we aren't putting in enough force to overcome the forces which are holding it together. Well, the expansion of the universe is putting like 10^-20 times less force into it than our arms would be.
This is a very different idea from "it's the same amount of space, but bigger", which is what I understand by the claim that a scale factor is increasing.
After some time, the scale factor of the universe grows, so that 1 new meter is 1.05 old meters. But, by hypothesis, as this happens, our meter stick contracts, so that it ends up being just 0.952 new meters (= 1 old meter) long. Why? Did the physical laws governing iron atoms change so that they pack more densely than before?
And if so, why do all particles pack at exactly the same new density? Shouldn't it differ from molecule to molecule?