Captain Gidday, that may have been the case in the Qantas study and if so just confirms studies from the late '80s and/or early '90s that showed similar results. Team make up and familiarisation counts for considerably more than pure fatigue.
It's been a long time since I've read many of those studies in any depth (probably 10 years or more) but I vaguely recall they were able to tweak the methodology to then do the sim with those 'teamed up' crew after rest (IE a few days after returning home) and it demonstrated significant improvement.
I do wonder why not much more was heard regarding that Qantas study from the mid 2000s. I left the 767 in 2006 and returned in 2008. In that time we suspended doing multi sector red eye tours of duty (e.g. PER-MEL-SYD, PER-BNE-SYD, etc). I was told that was as a result of the study but don't recall ever having read the rationale.