If I found myself in this situation, I'm going to accept the coach's explanation and let the team play with four on the floor and then file a full report with the state after the game and let them sort it out.
It's not my job as a game official to enforce the eligibility rules. I enforce the game rules. The game rules require 5 on the floor if there are 5 eligible players but we only have 4 and determining otherwise is beyond the scope of my responsibility.
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