Jeremy --
Yes, and the fix is very easy. Do the following:
1. Log into PWA with Administrator permissions
2. Click the Admin menu
3. Click the Manage Users and Groups link
4. Click the Groups link in the sidepane
5. Select the Project Managers group and click Modify Group
6. In the Categories section of the page, select the My Organization
category from the list on the right
7. In the Permissions grid of the Categories section, deselect the Allow
permission for Save Project and make sure neither Allow or Deny is checked
8. Click the Save Changes button
Completing the above steps will allow each PM to open his/her own projects
Read/Write but each PM will only be able to open everyone else's projects
Read-Only. Hope this helps.