Sorry - I thought you misunderstood as the links you referred to all discuss problems with sending emails.
OK, so you are saying that it is very common for the CF7 JavaScript to all work fine (I.e. displays error messages, sends confirmation emails etc.) EXCEPT just the one function of displaying the "success" message.
Even this function must be running to a point, in order to set the correct CSS class of "wpcf7-mail-sent-ok" on the message DIV.
As it still happens when I disable all other plugins and use the twentyfourteen theme, where do I go from here to find out what's happening?