> No subgroup is inappropriate unless you know all of the values of all of the parameters

I don't know how to put it less bluntly: you're incorrect.

> But sure, the intent they tried to demonstrate (take all sub-group analyses with a grain of salt)

That's not what they intended to demonstrate. They intended to demonstrate that you need a _reason_ to want to split, and that reason needs to be given _ahead_ of the analysis. If you see the results _and then choose_ a new data analysis (that includes new subgroup analyses), your procedure is no longer statistically sound.

This is a specifically bad statistical practice called HARKing https://en.wikipedia.org/wiki/HARKing