@vitnir I investigated sending Direct (Private) messages in AndStatus: they are done correctly using ”direct_messages” API that should ensure the message will be interpreted as a private message on a server side.
As I see @kassiopeia sent you public message, and this is why you had "Reply” menu item in AndStatus in the first place. For private messages you would not have the Reply option, only ”Direct message”.
In addition, testing Direct messages on Loadaverage.org server, I found out that this feature doesn't work properly: the server posts my Direct message successfully, but obviously encounters some internal problem and return HTTP 500 INTERNAL_SERVER_ERROR.
Conclusion: confirming what I was told earlier by GNU Social developers, Direct messages in GNU Social (almost) don't work.