I've been researching this problem for an hour now and it's getting kind of frustrating. I have a project in Bugzilla that I need to give read only access to some users (our BRM team). When I go to groups, I only see two checkboxes: "Can add to this group" and "member of this group". When I'm googling this, though, other people manage to have three checkboxes: "Can add to this group" "Is a private member (write access)" and "Is a public member (read access)". The post I saw with that info was from 2005, and we're on version 4.4.2 now.
Now maybe I'm using the wrong approach altogether. My current line of attack is to use the group memberships to make them simply a read only member of the group. But I'm open to any other possible way to accomplish this, including custom scripting.