Suppose School A has, because of local population or because of explicit selection, a distribution which is shifted one standard deviation above the population distribution. [...] this seems to be roughly the scenario we need to make the school's statement true.
Yes, that's about where the math came out for me, too - that you'd need a 1SD shift of the mean, but a similarly-spread normal distribution. I don't know that you'd keep the same standard deviation, though - there just aren't that many kids at the very top end to spread the curve out. I guess if it's just a selection effect, rather than some sort of floor, maybe.
Ah, nevermind, I know what the issue is. 95th percentile to 99.9th percentile looks like a small range. Converted into standard deviations, it's an enormous range. Like saying, "the top 50% of our kids fall between the 50th and 95th percentiles, so your 95th percentile kid will be in good company." 
