Well, I think that all of the above discussion does go to show that there is significant disagreement / confusion about the exact procedure of the Japanese rules.
While there are many other nuances and considerations, I think that a fundamental difference between the Japanese rules and various area scoring rules is the following:
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Under various area scoring rules, life and death status is determined by the skill of the players, by playing out any disputes.
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Under the Japanese rules, life and death status is determined by the rules. The concept of “hypothetical play” refers to determining whether or not stones can be captured under perfect play, and this process of adjudication should not (in principle) be limited by the skill of the players (i.e., if a skilled arbiter stepped in to resolve a dispute, then I believe that they should provide the correct judgements, even when both players have gotten the status wrong).