Excess groundwater extraction already causes numerous issue across the globe without considering a small effect on the Earth's tilt. Surely you don't need to accept any of the climate change science to accept that making the world a better place, doing less harm and using limited resources at a slower rate is a good thing. That's just simple thoughtfulness, common sense and good planning (all things humans are often terrible at).
Observations matching predictions is junk science.
We don't need this story to care about water usage...