I have the following controller:

class InvestorController extends Pimcore_Controller_Action_Frontend {
  public function defaultAction() {
    echo 'test';
    $this->disableLayout();
  }
}

With a document assigned to it:

+-----+----------+------+-----------+------+-------+-----------+--------------+------------------+-----------+------------------+--------+
| id  | parentId | type | key       | path | index | published | creationDate | modificationDate | userOwner | userModification | locked |
+-----+----------+------+-----------+------+-------+-----------+--------------+------------------+-----------+------------------+--------+
| 183 |        1 | page | investors | /    |  NULL |         1 |   1311069887 |       1311255788 |         1 |                1 | NULL   |
+-----+----------+------+-----------+------+-------+-----------+--------------+------------------+-----------+------------------+--------+

I'm logged in with this user:

+----+----------+------------------+----------------------------------+-----------+----------+-------+----------+-------+----------------+--------+
| id | parentId | username         | password                         | firstname | lastname | email | language | admin | hasCredentials | active |
+----+----------+------------------+----------------------------------+-----------+----------+-------+----------+-------+----------------+--------+
| 47 |       16 | test@test123.com | ec5f3078c69fb17197c6fcf0580a87b4 | NULL      | NULL     | NULL  | en       |     0 |              0 |      1 |
+----+----------+------------------+----------------------------------+-----------+----------+-------+----------+-------+----------------+--------+

Who belongs to this group:

+----+----------+------------+----------------------------------+-----------+----------+-------+----------+-------+----------------+--------+
| id | parentId | username   | password                         | firstname | lastname | email | language | admin | hasCredentials | active |
+----+----------+------------+----------------------------------+-----------+----------+-------+----------+-------+----------------+--------+
| 16 |        0 | Site Users | 311c1c54c7ea1c273a08918bb52eddd5 | NULL      | NULL     | NULL  | en       |     0 |              0 |      1 |
+----+----------+------------+----------------------------------+-----------+----------+-------+----------+-------+----------------+--------+

Neither of which have any permissions:

mysql> select * from users_permissions where userId in (16, 47);
Empty set (0.00 sec)