Psu supplies power to the motherboard and everything else. All of that is grounded to the frame by the 9 (ish) motherboard standoff screws. The frame is attached to the psu by the 3-4 screws in the back. The psu itself is grounded to its own case, which is then attached by those 4 screws to the frame. The psu ground originates at the plug from the wall.
So the only real potential failure points for ground are the wall socket itself, many older electrical systems didn't use a ground, just a 2 prong, hot/neutral setup. The cord, if the ground pin is broken, or the wire inside the cord is broken, no ground. The physical connection from plug to case inside the psu.
The chances of failure (usually due to excessive paint) from 13 different screws all simultaneously not supplying a decent ground are remote at best.
The only other option, it's not a grounding issue, but a you problem. If you contain excessive amounts of static electricity and touch a grounded appliance, you become a grounding path, and get shocked.