I've come across a function that I think may be wrong.

Consider changing

   public function inGroups(array $groups) {
      foreach($this->Groups() as $group)
         $memberGroups[] = $group->Title;

      return count(array_intersect($memberGroups, $groups)) > 0;
   }

To:

   public function inGroups(array $groups) {
      foreach($this->Groups() as $group)
         $memberGroups[] = $group->ID;

      return count(array_intersect($memberGroups, $groups)) > 0;
   }

To check a member's permissions by group Title is unreliable as a title can duplicated.

Yeah tested on an instance with multiple groups. Will submit as patch.