Setting Drupal permissions doesn't get picked up by CiviCRM if its language is not English.

Setup a CiviCRM and have it in one language only, and not English. In my case the only language in CiviCRM was Dutch.
Create a Drupal role: CiviCRM Admin and assign it some permissions (Access CiviCRM at least)
Assign the role to a Drupal user and log in, click on the CiviCRM link.
You'll only see the Home and Help tabs available (in their localised language because CiviCRM is not set to English)
Log out, then log in as admin.
Add English in the administer->general settings->localisation and switch to it.
Log out, then log in as the user with the CiviCRM Admin role.

You will now see the tabs. The bug is that a switch of languages is needed for the tabs to be displayed.