Yes, it is a fresh new install.
This is an image of the right-click menu on one of the folders with sub-folders:
Searching through the log files, I noticed that Zimbra considers all these parent folders as exempt from syncing. There are entries of this type:
log/zdesktop.log.2009-01-09:2009-01-09 07:53:49,749 DEBUG [mid=2]  datasource - Local folder '/Inbox/compstuff': Synchronization disabled for this folder
So there are two questions: Why does Zimbra believe this? And how can the sync flag be changed for these folders, seeing as there is no option to do this in the menu?