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Stuart_Armstrong comments on No independence of irrelevant alternatives (picture proof) - Less Wrong
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If you're postulating a (much much) weaker version of IIA saying something like "if you remove symmetric irrelevant points from a symmetric set, the outcome doesn't change" then you'd be right. But IIA does not require that symmetry be preserved.
Yep, I agree that strong IIA of "if x is chosen from T, and S is a subset of T, then x is chosen from S" doesn't apply if preferences are based on the relative merits of x rather than the individual merits of x. That statement seems obviously true on its own, and so I think the picture proof of this particular example detracts more than it adds, because there is a natural weak IIA here.