True, but there should be some rationale as to why they assume that normalization wrt the cofactors they've chosen are sufficient to provide for their conclusions.
Simply seemingly randomly choosing cofactors and then shrugging it off as good enough to draw conclusions from is sloppy. Typical, yes, but mean you shouldn't be skeptical of their conclusions, no.
Your specific concern was about socioeconomic status and because they answered that you now call it a random cofactor. Come on. You're not giving meaningful criticism. You're just being negative.
Simply seemingly randomly choosing cofactors and then shrugging it off as good enough to draw conclusions from is sloppy. Typical, yes, but mean you shouldn't be skeptical of their conclusions, no.