Rules: Is this position a draw? Is this position a draw?

[FEN ""]
1. Nf3 Nf6 2. Ng1 Ng8 3. Nf3 Nf6 4. Ng1 Ng8


I don't mean to ask the age-old question "Is chess a draw?"; four moves have been played here, returning to the starting position. Since the start position has appeared three times, it seems that white can claim a draw by threefold repetition. However, lichess does not permit this claim, which got me thinking that perhaps there is a subtlety to the rules.

FIDE says:


  9.2
  The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not necessarily by a repetition of moves):
  
  a. is about to appear, if he first writes his move, which cannot be changed, 
  on his scoresheet and declares to the arbiter his intention to make this move, or
  
  b. has just appeared, and the player claiming the draw has the move.
  
  Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:
  
  
  at the start of the sequence a pawn could have been captured en passant.
  a king or rook had castling rights, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.
  


It seems that white clearly has the ability to claim a draw by 9.2.a, since 5. Nf3 would definitely repeat the position after 1. Nf3. But my question is really whether 9.2.b applies for white (or perhaps equivalently whether black can claim the draw on move 4 via 9.2.a): Did the starting position "occur" before 1. Ng3? Or does it somehow not count? Are the rules ambiguous?

Obviously this is a silly game, but this kind of "Fool's Draw" might occur in practice when both players want a draw but are not allowed a normal offer (e.g. FIDE world championship 3.8.3b "The players cannot draw a game by agreement before black’s 30th move.").
This is a better question than it seems at first glance.

Intuitively it seems possible to claim a draw, since the position appears to have occurred three times.

However, according to a strict reading of the rules, the position after 4...Ng8 has appeared only for the second time. The relevant clauses are 9.2:


  [...] Positions are considered the same if and only if the same player
  has the move, [...]


and 1.1 about the start of the game:


  The player with the white pieces commences the game. A player is said
  to ‘have the move’, when his opponent’s move has been ‘made’.


In the starting position, white does not "have the move" since black did not make a prior move, white merely commences the game. Therefore, the positions before 1. Nf3 and after 4...Ng8 are not the same, and a draw cannot be claimed yet.