The fact that anything goes doesn't give the untrained individual an advantage. In fact any additional tools gives the person with more training the advantage. Concrete floor? Good thing I know how to get a double leg and slam. Also I know how to defend takedowns so it's entirely to my benefit. Headbutt while performing an armbar? Pretty sure the thigh restricts that. And for the most part. biting and hair pulling ain't gonna do much when adrenaline is pumping.
The only advantage for the untrained combatant would be a weapon.
I think I was pretty clear in saying the more controlled the fight the more the trained fighter has the advantage. Also I said the trained fighter has the advantage either way just more so when it's controlled. Which IMO is all 100% true.