Ah yes, the definitive answer, does one exist for a complex situation?
I don't have an answer for you, as I can see merit in both arguments. Let's look at the reality of what the real world gives us, and see if that helps.
1. I've never seen threaded plastic standoffs provided with a PC case or mother board, or even sold individually, but metal ones are commonly available. Metal is not needed for strength in this application, and plastic would be strong enough for this application.
2. Some cases I've used provide screws for the mother board, that are painted black, including the threads. I've also seen painted standoffs. Paint is an insulator, and if we needed an electrical connection through those screws, a bad choice. I use both plain and painted screws in PCs I use, with no difference I can see.
3. In electrical theory, the flow of current in a circuit, when multiple paths are available, will always be through the shortest path, given equivalent resistance, or the one of least resistance. Does that not imply that all available circuits/paths (grounds) will not have a current flowing through them, or be "used"?
4. I have never seen a warning or instruction stating that you must insure a ground between a mother board and the PC's case.
5. Electrical power to a mother board only comes from the PC's power supply. Obviously there must be ground connections maintained by the mother board between it and the power supply. Given that, why do we need more?
6. In audio circuits, it is believed that multiple, independent ground paths can create noise (hum.) That is not only for audio signal carrying circuits, but power source circuitry. In this case the use of a "star ground", where many if not all ground circuits/wires are connected together at one point (creating the "star"), and from there on one wire/conductor to the final ground/earth connection, is considered superior.
7. I think I have noticed in every mother board I've owned, that around the screw holes there is at least some solder or other metallic material on the top of the board, that would contact a screw. There is nothing like that on the bottom of the board. But do we really know if they are connected to the boards ground?
IMO, each of these "facts" point to either Yes or No need for grounding through mother board standoffs. IMO, the tally looks like this:
YES: 1, 7
NO: 2, 3, 4, 5, and maybe 6
Otherwise, the best I can find and makes sense is this: There are two kinds of ground, one to complete any circuit connection, and the second is the protective earth/ground. The first is essential, but is not related to connecting the motherboard in general to ground. The second is an added safety feature, given (assuming) that you can electrically connect the board to the case with standoffs and screws.
So, not essential and at best a safety feature.