Bang! Elimination Award For Henry Block and Backfire
The FAQ says:


  Q05.  Who  is  considered  to  be  responsible  of  the  elimination  of  a  player  with  cards  like Indians! and Gatling?
  
  A.  Unlike  the  Dynamite,  the  player  who  played  the  Gatling  or  the  Indians!  is  considered  to  be  responsible of the elimination of a player. All special actions due to this elimination apply to him (for example, if he just killed an Outlaw this way, he draws the 3 cards reward).


Based on this, it appears that any time a player's card or ability directly causes the elimination of another player, the player is responsible for the elimination (and draws the outlaw bounty if the eliminated player was an outlaw).  Thus, both Backfire and Henry Block's ability would allow a player to draw three cards if that player eliminates an outlaw using them.