So in 2012 we started asking for SAT and ACT scores, which are known to correlate well with IQ and are much harder to get wrong. These scores confirmed the 139 IQ result on the 2012 test. But people still objected that something must be up.

Not quite. The averages might roughly work, but the correlations appear off. For instance this:

SAT score out of 1600/IQ: .369

Is about half of what you'd expect.