I'll admit I haven't dealt with wedding registries much at all (really, I watched somebody use a registry kiosk at a store once and that's about it) but I was always under the impression that registries are generally pretty much public.
For example, at Amazon Universal Wishlist, the ID of a valid wishlist is very hard to guess -- like 6HV8XSTGDT3E7-difficult. On top, you can select whether you want that list to be public (discoverable via name search), visible if one knows the link, or private.