For some reason on Profile -> Friends page, the post of the profile owner have been duplicated to his/he friends. We tried to activate all other plugins and change the Theme and it seams to have the same problem everywhere. The only thing which makes the difference is when we deactivate Buddy Press Media plugin we are getting broken links instead of duplicated messages.
You can check for yourself:
http://ucgym.com/members/oksana/friends/
OksanART message is duplicated to her friends.