Threefold repetition in view of castling rights In view of castling rights, an aspiring rules lawyer could ask: when does threefold repetition support a draw claim? Technical example:

[fen ""]
[title "Illustration of castling rights"]
[startply "13"]
[startflipped "0"]

1. e4 g6 2. b3 Bg7 3. g3 BxRa1 4. e5 b6 5. Na3 Bb7 6. Qg4 BxRh1 7. Nc4 Nc6 8. Kd1 Nb8 9. Ke1 Nc6 10. Kd1 Nb8 11. Ke1


The aspiring rules lawyer's question is not actually my question today. My questions today rather are these:


Has an arbiter ever expressed an opinion, given advice or issued a ruling regarding threefold repetition in view of castling rights?
Have competent persons in any chess federation ever discussed the matter?
Do parallel or otherwise related laws, opinions, advice, rulings or discussions by arbiters, federations or competent persons exist that indicate the principles by which such a case might be judged?


The three questions are related and answers to any or all of the three&mdash;or even partial answers to any of the three&mdash;would be read with interest. I seek insight into how chess authorities have approached (or would approach) such problems.

Related question here. Related answer here. FIDE's laws of chess here.

UPDATE

The excellent, concise, informative, well-researched answers of @BrianTowers and @TonyK, taken together, perfectly illustrate the reason the question has been asked. Both answers are recommended and, naturally, both have been upvoted by me. Ironically however, under the circumstance, neither answer can be accepted over the other, can it, for only the two answers together serve to illustrate the point.

Since the two answers so perfectly capture the two sides, my preference would be that further answers (if any) avoid taking sides but rather focus on the three items listed above.

ILLUSTRATION BY @REMELLION

Incidentally, before the question was asked, @Remillion had composed a problem position to illustrate a related point. He had originally meant the position as a joke but, since he has mentioned the position in comments in the present context, we can diagram it here.

[fen "B6N/1p1pp3/4pp1P/7P/7P/2p4P/1PPP2rr/R3K2k b - - 0 1"]
[title "By @Remellion: black to move; helpmate in 2"]
This is dealt with explicitly in article 9.2.2 -


  9.2.2 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:
  9.2.2.1 at the start of the sequence a pawn could have been captured en passant
  9.2.2.2 a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost
  only after the king or rook is moved.


Neither of white's rooks move hence castling rights are not affected until the king moves. 

In general provided white has not moved his king he may castle on the side on which a rook which has not moved has been captured. I believe there are even puzzles which rely on this for the solution.