The post gives an example of an SPR that uses weighted cues. But he specifically says

This particular SPR is called a proper linear model,

indicating that there are other types of SPRs, and I currently have no idea what those other types might be.

I agree with you that complicated statistical tests can lead to spurious results; simple statistical tests can also lead to spurious results if the person using them doesn't understand them. I naievely associate both of these with "the test was designed to correct against a different type of flaw in experimental design than actually occurred".

When the focus of the statistical test is on accurately modeling a given situation, I think it is less difficult to realize when a model choice makes sense and when it doesn't, so more sophisticated approaches will probably do better, since they come closer to carving reality at its joints. This might be an inferential distance error on my part, though, since I have training in this area, so errors that I personally can avoid might not be generally avoidable.