That IQ tests are unbiased across groups is highly implausible and empirically unsupported.

There are a very narrow set of technical conditions which let you out of this, i.e., which let you combine group differences, measurement unbiasedness and predictive unbiasedness. (See Millsap's papers for details.) That IQ tests satisfy them is highly implausible, and, to say the least, empirically unsupported.