The issue at hand is how LinkedIn defines “public”. From the public profile settings page the author linked:
> Select what shows via searches on Bing, Google, etc. as well as on public profile badges and permitted services like Outlook, when the viewers are not logged-in members or did not bind their LinkedIn account to their account on such services.
Its not anyone who isn’t logged in but rather a subset of unauthenticated users who discover your profile through a specific set of avenues
Clicking on the informational icon next to “public” reinforces what they mean:
>All LinkedIn members as well as others who find you through search engines (e.g. Google, Bing) or other servies.