Partly paranoia, and partly because overrated doesn't mean worthless. I occasionally advise startups we've funded to keep some part of their plans secret. (You never want to keep everything secret, or it just advertises you're keeping a secret.)
Fortunately, YC folks have you to advise them. I often find myself in the predicament where I need to discuss an idea/ get some feedback / advice from someone who's familiar with the startup scene. Friends - family are too out of touch with tech startup world to provide any relevant,useful input.
I'd say YC should start like a monthly session (paid) where a limited set of entrepreneurs can get advice/input? Maybe far stretched considering your time constraints, but just thinking out loud.
Yeah, I think a lot of it are delusions of grandeur and fear that people will mock the ideas. Note--stackoverflow.com was very open all along, very successful, and as far as I know virtually no competition.