Rock by itself will process nutrients, because it has both aerobic and anaerobic bacteria, so what started out as fish food will end up as nitrogen gas which will be expelled at the water surface, however, when people implement sumps they end up using some sort of mechanical filtration like a filter sock or floss pad, which gets very dirty, very quickly. The same goes for canister filters- they recommend cleaning them weekly so not to have a nitrate build up from all the detritus sitting in them.
Without either of these methods of filtration, where does all that stuff go? Does the rock break down particulate matter to nothing? Perhaps some, but every piece of filtration helps as long as it's maintained properly. Mechanical filtration is a benefit, as long as you clean it regularly.
It's quite possible to run a reef tank with just live rock, but it would depend on the tank, the bio load, the keepers husbandry and feeding habits, the type of food, the flow, the amount of rock, the type of rock...there are more variables than a yes or no answer.
