Do Jehovah's Witnesses believe that their "Governing body" will rule the world after "Armageddon"? I understand that Witnesses follow an unelected body of men called a "Governing body".  However I'm unclear on whether or not they believe this governing body is in charge of the earth after their claims of Armageddon.  Is this true?
Read this article: 


  http://www.jw.org/en/publications/magazines/w20130715/who-is-faithful-discreet-slave/
  
  This addresses your question specifically.


Often you won't get the same answer when asking random people from their congregations as some are more in touch with modern developments more than others, as you've just discovered.

Another thing is that the interpretations on core modern fulfilments often change: 2013 changed the governing body's role slightly. The "wheat and weeds" understanding also recently changed.

The answer is "No" they do not believe they will exclusively "rule the world", but are part of the 144,000 which serve as Kings and Priests under Christ, obeying him as co-rulers. They presently find themselves to to have a unique role among the anointed, that having changed to "Faithful and Discreet Slave", which dispenses food (teachings) in due season/proper time.