Barsel - I'm sure you'd agree that having a baby and enjoying relative privcacy (there's that word again!) is a lot easier to keep from prying eyes than pretending to miscarry a baby, and expecting that to stay secret.
I simply don;t believe it's possible - it just becomes a ludicrous, and deeply unpleasant, conspiracy theory.
As Mr Lincoln said, and it's as true now as it was then - three people can keep a secret, but only if two of them are dead.