Why can't my user see anything in the left navigation, even though they are assigned to Projects and Tasks?

The answer is that, the permissions and resource assignments to project and tasks are independent.  For example if I have a contractor or customer using the system and updating tasks they are assigned to, they can update their tasks, entering comments and time via the My Insight Dashboard without being able to see the project or anything else in the system.  If the user that cannot see the folders in the left navigation is not a customer or contractor then you probably want them to have at least Read Permissions to your folders.  The video in this article goes into more detail.