I consult for a specialty coffee shop, and in my experience the electrical ground of the machine has no impact on static generation - I doubt the burrs themselves are grounded. The amount of static you get very much depends on the specific grinder you use. Our large-batch shop grinder creates massive amounts of static and requires water to be added to not end up with a mess, while our espresso grinders tend to generate less.

To your second point, one of the fascinating things about this study is that the static charge during the grinding process causes the coffee to clump - that means that by the time the water hits the coffee puck it is too late to avoid the static-induced clumping.