Can a joker be played on its own?
Your opponent is confused. As you can see in the rules: 


  The Joker:There are two jokers in the game. They can be used for any
  tile in a set. A joker used in theopening set scores the value of the
  tiles it represents. A joker can be retrieved from a set on thetable
  by a player who can replace it during his turn with a tile of the same
  numerical value andcolor it represents. The tile used to replace the
  Joker must come from a player's rack and notfrom the table. In the
  case of a group of 3, the joker can be replaced by the tile of either
  of the missing colors. A joker that has been replaced must be used in
  the player's same turn with 2 or more tiles from his rack to make a
  new set. Players cannot retrieve a joker before they have laid their
  initial set(s). A set containing a joker can have tiles added to it
  and can be split apart or have tiles removed from it. The joker has a
  penalty value of 30 points if it remains on a player'srack at the end
  of a game.


You can play a single joker from your hand. But, if you replace a joker with another tile, you have to play it with two tiles of your hand.

So you can play the joker.