I cannot see any reason not to use rivets, as long as you can get them to grab and not get pulled out. Just wrap with the Aluminum tape. The screws are just a PITA. I hate trying to deal with them in tight places.
As for the Fire Marshals, they all want no one to burn anything down, but they never realize that that also takes away job security. If no buildings caught on fire, there would only be medical emergencies and no need for a bunch of Smoke Eaters and stations, doing nothing.
My thing about the grounding, is that it is hard to get a ground point ran, if you are dealing with a building on a slab, apartment, condo or finished. In commercial operations it is a given. In homes it is one of those things you really have to plan when you are running wiring.
The sad thing is with all of the plastic that they are putting into washers and dryers these days, there is not much to ground, other then the vent pipe, since it used to use the actually metal of the duct that was screwed to the chassis of the dryer, that would bond it to the Electric Neutral or ground point.
I need to take mine apart, since it sounds like it has one of those darn air soft balls inside at the blower. Just have not been able, since my son is off at school.