You identified LN6.5.1 as the client SW, but is the users' mail file template using an R5 or R6 template design?
Secondly...have you checked the database properties of the users' mail file? Look under the "Design" tab and the "Advanced" tab for the relevant options.
R6 mail template design has the cache sored on the server side, hence read/unread are more easily handled. The R5 template design has the cache stored locally on the client, hence the reason to press the F9 key option to sync these read/unread options.