There appears to be some confusion over public and private shares. Generally to access a public share one does not need to enter in a user name and password to access the public share. All users have full read/write access in a public share.
Generally for a private share one must enter in a user name and password in order to access the private share. It won’t matter what setting (read only, full access, no access) a share has. If set to Private then either one cannot the contents or they have to enter in a user name/password to have either read only or full access to the share contents.
With a public share, anyone who accesses your local network will typically be able to access and see the public share’s contents.
For example WD by default creates a single public share called Public. Officially one cannot set the share called Public to private. Hence there will always be one share on your My Cloud that is Public and can be accessed by anyone on the local network. Unofficially there are various ways other users have tried to either hide the share called Public or configure it so it’s a private share.
One additional note. When Media Serving is enabled on a private share that media will be accessible to any DLNA client on the local network. The DLNA protocol/standard does not recognize user permissions on files/folders. If there is media you do not want to be shared to DLNA media clients make sure to turn off Media Sharing for the share in the My Cloud Dashboard.