I need to stress the following:
- in the analogy "bolt" corresponds to "spring".
- Also, please note that the setup involves a bolt connecting two plates. The external load is applied on one of the two plates (not on the bolt itself).
So I guess what the article is saying is that
- you preload the bolt (e.g. 1000N). The preload has the effect that now the two plates are compressed. I.e. they thickness reduces and as a result they exert a force to counteract the preload.
- When you preload the bolt, the bolt maintains that load as if it is statically loaded. The load increases only if the force applied on the plates exceeds the preload (1000N in this example).
- When you apply an external load then that force has the effect, that it contributes to the force equilibrium. I.e. the plates are less in compression. In the extreme case (e.g.if the applied force is 1000N , then the plate is not in compression any more).
- If the preload (e.g. 1000N) is exceeded then and only then the bolt experiences any additional force.
So the idea is that you preload a bolt to a high value (close to 80 or 90%) of its strength, and then let it work its magic.
The reason its best to have such a high value (80-90%) is because then the two plates are less probable to come out of the compression state. Additionally you make a very efficient use of the bolt.
If the plates stop being in compression, then they will become separated. If the load is dynamic you'd have a structure that will very soon after fail due to fatigue loading.
Why preloading is better than not. (UPDATE)
The reason why (not preloading the bolt) is worse, is primarily a) fatigue and b) possibly impact loading.
fatigue
You are probably familiar with S-N curves showing life vs stresses (see below for a typical one). You can see that the static case can sustain much higher loads compared to the multiple cycles of loading and unloading. (I'm sure you've managed at some point to cut a wire or thin sheet just by repeatedly bending it).

So preloading the bolt, and having it sustain a constant load throughout its life is actually a good thing.
Impact loading.
This is something that is a possibility if the application and removal of load is abrupt. One example I've witnessed it, is on bolts of solar panels in windy regions. It the load is not properly preloaded what happens is that the load on the panel could result in exceeding the preload. In that case the bolt extends more (like a spring) and a gap is formed. Assuming that the bolt doesn't break (lets say its only 30% preloaded), because the wind gusts can change in intensity very very fast, that panel will return to its original position. However, it will convert all the elastic energy it accumulated to kinetic, thus a potentially very high impact shock on the structure (and on the bolt).