You make generally reasonable points, but in that case, why include the clause at all if nobody would have suspected it would have been an issue anyway? It's there for some reason, assuming this third-party does exist, such is the current level of scepticism.
Out of interest, how would a club go about finding out the identity of this alleged third party? Presumably the participation agreement signed away any legal rights of knowledge or enquiry they might have had? Maybe that's not the case at all, but if it is, it effectively gives the FAI the freedom and protection to claim what they like.
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