Can a static electricity shock damage a DVD disc?

Unless the static shock is a lightning bolt, no.

My answer is NO but please don't store them on top of an electrostatic generator.

I usually store mine under a tesla coil and so far so good.

I dunno. But you'd think from the scratched up rental discs I get from Netflix, virtually everyone was trying to rub the damned things against the wall to make them stick by static electricity.

What the hell is wrong with people and the way they handle rental discs?

That would have to be one hell of a static discharge to damage the disc. Probably something big enough to melt the plastic. I certainly wouldn't expect to see that kind of damage under normal household conditions.