There are Signature Moves, and there are signature moves.
The former is a specific move that, generally speaking, "belongs" to a Pokemon of significance, generally but not always a Legendary or Mythical Pokemon. Examples would include Dialga's Roar of Time, or Darkrai's Dark Void. These are moves that no other Pokemon is capable of using, even if they are somehow able to learn it (Smeargle and Sketch being the primary pathway). The move will always fail when used by a different Pokemon.
The latter are moves that happen to have a specific theme relating to a Pokemon, but do not belong to that Pokemon. Many Pokemon tend to be able to learn such a move, but the initial creative idea was for it to mesh with the theme of a specific Pokemon. Water Shuriken is a good example, as it was developed for Greninja for obvious thematic reasons. But other Pokemon can learn it, like Accelgor. They tend to be more rare when the move is first created, but then are handed out more readily as time goes on.