Within Prospector, expand down to your structure list. Then right-click on one of the structures and look at Edit Style. Are you using a block to represent your structures, or a object outline? If you're using a block, it might be possible to have that block defined on another layer that isn't turned off and might still show.
I guess the question I have is, if you want to show structures and pipes, why not turn on the network's parent layer?