Should an arbiter intervene?

[Roger Lancaster]

One U8 player claimed his opponent had made an illegal move and the opponent denied that he had. The players could not agree the relevant position (no scores as it was rapidplay). Neither player wished to continue with the game. In retrospect it was a mistake not to apply the normal laws of chess and insist the game be replayed (or continued).

Exactly - although recognition of the fact should not have required retrospection.