I don't think your reasoning is valid. A test might be unable to discriminate accurately at the extremes not because it's uniformly too inaccurate but because it doesn't have enough range.

Toy model: the test consists of one question that everyone in the top 1% can do and no one in the bottom 99% can do; one question that everyone in the top 2% can do and no one in the bottom 98% can do; ... one question that everyone in the top 99% can do and no one in the bottom 1% can do. This test discriminates very nicely and accurately throughout its range of applicability, but it will do no good at all from distinguishing a top-0.01% person from a merely top-1% person.

(Just as a tape measure 2m long will let you compare people very accurately by height provided they're no taller than 2m, but will be much less useful for people taller than that.)