I don't doubt that this is, as she says, "statistically remarkable" given how rare IQs of 132+ are - but this still means that more than half of the children concerned did not have IQs over 132. This is hardly resounding support for the accuracy of parents' identification...
I have seen several other sources for similar claims, but I haven't yet found one that stood up to even cursory examination. E.g. Gross's book cites a paper from Gifted Children Quarterly (vol 18 pp202-09) which does indeed say that parents were effective at identifying gifted children - in the sense that most children who turned out to be gifted had been identified as such by their parents; but unfortunately, more than half of all the children had been identified as such by their parents! (So you could say parents were effective, but not efficient. Teachers missed more gifties, but they nominated far fewer children overall.)
Ok, I'm playing devil's advocate here.
But we don't know the distribution. Maybe the other half were right below the 132 mark. Also some of those kids could be 2E and don't have their IQs show up well with testing. There's probably at least some of those kids that had a bad day too. Also... testing between 2-5 is pretty inaccurate so I'd think that you'd probably have a big problem with kids that didn't comply with testing.
