It depends on what exactly you mean by "only visible"; the act of browsing a computer is distinct from being allowed to access its shares, whether read-only or under full control.
With that in mind, there are actually 3 security levels on a share: browsing, read access, and full control.
Check group policy application (install and use the GPMC, it beats the old crappy system by a mile and a half), verify the entire top-down DACL tree for your share's physical location, and check the exact application and inclusion of all users and groups that have access to the share (not the physical location).
Unless you want to, as you said, prevent people from even browsing to a share, share access should typically be left at Everybody - Full Control; actual access control is better done through the filesystem.