Depends on the life cycle and type of parasite.
What makes you think there is nothing for the bacteria to feed on? Isn't one of the supposed benifits of using NSW (apart from the cost), that it is full of "life" which you don't get with ASW? Also a lot of bacteria don't die immediately when there is nothing to feed on. They can go into a dormant state (spore like state), and stay that way for many months, then spring to life based on environmental triggers.
Really to kill bacteria and parasites effectively, you have to nuke them. They don't kill themselves very easily, or quickly.
It's not obvious at all, and seems kind of a strange statement. Just because you leave the water sitting there, the bacteria dies off? I would actually think the opposite, you'd get an increase in bacteria, as the zoo-plankton in the water dies.
Layton