Mike,
The way you removed the message is by removing the ability for Joomla to display any system messages.. Those messages can be good a lot of the time, to tell the user their Password is invalid, account wasn't found, they subscribed to a forum post, etc.. Any of those blue/red bar messages are system messages.
I'm not sure where that LOGIN_SUCCESSFUL message is coming from (It's not part of JFBConnect or Joomla, that I can tell). However, you may want to try to figure out what extension is adding that and remove the message from it directly. That way, your system messages will still show.. but those should be for more rare events.
Hope that helps,
Alex