Can visit the page but can't see the tab it should have
Drupal doesn't show tabs when there is just a tab defined or visible for the currently logged-in user (which includes the case users don't have the permission to see other defined tabs).
If you look at what Drupal does, for each node there is node/%node/view and node/%node/edit; when users don't have the permission to edit a node, they don't see any tab, in the node page.

See the following screenshot, taken from drupal.org at https://www.drupal.org/node/5, using an account with the permission to edit the node.


  


You see the View, Edit, Outline, and Revisions tabs.

Compare it with the screenshot taken using an anonymous user account, for the same page.


  


You don't see any tab, but the screenshot is for the View tab.  In fact, if you try accessing https://www.drupal.org/node/5/view as anonymous user, you would see the same as in the last screenshot.