Normally I wouldn't bring this up, but since you're touting your scientific credentials: no, that doesn't follow! Not even close!

All it says is that gender is not wholly determined by sex. That doesn't mean it's not partly or even mostly caused by sex...or completely caused by differential sexual determination of some tissues (e.g. brain or part thereof). The only thing that's ruled out is that sexual differentiation of reproductive organs and obvious dimorphic physical characteristics completely determines gender.

If we use a bunch of other evidence, then we can refine our understanding, but please don't besmirch science by donning the science-hat and then engaging in extremely sloppy reasoning and/or argumentation.