"Geologists studying growth rates of the Sierra Nevada and of central California’s Coast Ranges have identified an anthropogenic contribution to the mountains’ uplift that they suggest is tied to the decades-long depletion of groundwater in the state’s Central Valley. "
Gotta love sensationalism. I don't see where the researchers said that humans were causing it, nor that they have identified anything. It does say that they came up with a theory, ran a single simulation, and that simulation matched the data fairly well. Hardly scientific proof. Considering the source, I would expect more science and less sensationalism.
In vegas, pumping of groundwater unambiguously lowered some areas-- though it was more like 5-20'. Drill heads on rigid casings were thrust 5-20' up in the air. But these were in gravel-fill areas, and had there was no effect for the nearby mountains. The definition of "sea level" is somewhat arbitrary, and with the new earth-centered datums, plate movement accounts for a larger change in the elevation of mountains.
As an engineer and land surveyor who uses GPS frequently, you would have a hard time convincing me that a gps receiver, even with excellent differential correction, could have a reliable vertical precision of 1 millimeter. Of the 3 coordinates a gps measures, the vertical coordinate is the least precise, primarily due to subtle fluctuations in the satellites orbits due to irregularities in the earths gravitational field. However, if you take data from a large array of gps receivers, throw out the datapoints that don't fit (not as dishonest as it sounds) and then go through some creative statistical analysis, you might be able to justify a 1 mm precision for your measurements. But I am still skeptical.