A Unity3D UNET example with a working version of SyncListString ([url removed, login to view]) with the following characteristics:
1) Use standard UNET code with NetworkBehaviour
2) Exemplify a working SyncListString that is synchronized between players
3) The ability to read any of the stored string data (based on index) in the SyncListString from any of the players
You can design this however you want as long as it shows the requested result.