Groundwater unloading and corresponding changes in fault zone stick-slip behavior
Changes in water level effect the pore pressure at depth around the fault. The general assumption is that the pore pressure is proportional to fault-normal stress which can be thought of clamping stress (i.e., the stress that prevents it from slipping). Basically the higher the clamping stress the more shear stress is required to make it slip. Now the shear stress on San Andreas accumulates due to plate motion between the North American and Pacific plates and that rate remains unchanged. But the normal stress can change slightly due to water level changes, so it can either advance or retard the occurrence of an earthquake in time. But under no circumstances can it stop them from occurring.

The main idea in the paper is that the normal stress on faults have slightly decreased (due to water level drop) which helps to unclamp the fault(s) which in turn increases the background seismicity rates.

So given all this, the first argument by (Holthaus) is correct. However the unclamping can also advance (in time) the occurrence of the big one. Having said that please remember that stress changes we are talking about are rather small.

With regards to the Napa earthquake: The point of an earthquake is to relive the accumulated shear strain. If there are two faults in parallel (as is the case in the region) and both are accumulating strain then an earthquake on one will decrease the 'effective shear stress' on the other fault, directly parallel to it. However at the same time it will increase the shear at the two ends. So things are slightly more complicated.