I think you are using "public" differently here than a lot of people would. A public bathroom is still "public" in that it's available to anyone and doesn't require specific information about you to use. However, most people would still consider it a private place, and expect their privacy to be respected while using it.
Is a government website a private setting? Is a personal blog private or public?
I wonder if other countries have already explored this and written some law about it.