From our point of view this is a bug but it seems a design choice by Drupal for their projects. (Not an ideal choice though, I think.)
Any administrator can create issue records but even if we have agreed who will do what the assigned person has to edit the issue themselves to update the assigned field.
This has aleady been added as a feature request, http://drupal.org/node/4354, and has some hacks that may work for our site.