Hierarchical Select Access

The Hierarchical Select Access module complements the Hierarchical Select module and offers a mix of content types and role permissions for selecting menu items in a hierarchy when creating content.

Download the module from Drupal.org:
Hierarchical Select Access

The module solves the granular role-based permissions problem discussed in this issue:

It has a settings page for allowing certain roles and certain content types to use Hierarchical Select. Roles that are ticked in the settings page will use the default Drupal menu items which are presented when creating new nodes.

Ideally the module should live in the Hierarchical Select module, hopefully in the anticipated Drupal 8 release.