The statisticians I knew were only too happy to go along with some ANOVA. They're usually consulted at the start of the study, but rarely co-author.
A lot of psychology is bad research. There's a reason there's a reproduction crisis. Statisticians are to blame for that, too. They've been teaching and using NHST, even though all arguments point away from it.
But statisticians can't fix a bad design, because they rarely know the factors involved, and they can't fix errors in the methods, because they've got no idea about the subject matter. The statistician in your argument comes across as some kind of totem.
> There's nothing there.
There's something there, but since we don't know what, it's best to take it with a grain of salt. However, if even the bloody HR department looks at IQ scores, it gets a lot of attention. And one explanation is that it predicts better than nothing. If you have to choose between two candidates, and one has an IQ of 80 and the other of 120, you know who (on average) who fits best.