Fireteam Recruitment Chats do not allow additional players to be invited.
Once a Fireteam chat has been created using the "Recruit Fireteam" feature in the Recruitment forums, only the players from the Recruitment topic may participate in that chat. If additional players would like to join, a new chat will need to be created with all desired players included.
This is also true of any private chat that is created on Bungie.net.
For information regarding Recruitment posts, please see: RECRUITMENT FORUM FAQ