Even if a role has no Structure related permissions, the "Structure" menu item still appears in the admin toolbar.
Selecting the menu takes the user to a page that simply states: "You do not have any administrative items."
It seems to me, that the top level menu item simply should not be present if there are no pages under it.
To reproduce, using a fresh installation:
- login as the site's superuser, and create a new role - name it anything you wish
- On the 'permissions' page for the new role, grant access to 'Use the administration pages and help', 'View the administration theme' and 'Use the administration toolbar'
- Create a new user for the site, and give this user the newly created role
- log out as the superuser, and login as the new user, with the new role
- notice that under 'Manage', you still have "Structure" - clicking it will take you to that page that states that you have no administrative items.