The bold part is almost certainly true, It's just that the fine margins in top level competition might mean that the differences that stem from other mechanisms and other phases of development (and not amenable to medical manipulation) may still mean this has the potential to distort some competititons. Unfortunately, I don't think conclusive evidence in this sort of complex biological issues can come from anywhere else but pure raw data from actual competition and these things can take years/decades. There are probably not enough transgender people competing yet to allow for well-designed research, but I expect this number to rise.
People who have to decide how to approach this in the meanwhile have a nearly impossible task in their hands. The disadvantages of other solutions (special categories, outright ban, etc) will have to be weighed against the risk that you "ruin" some top-level sports for a while until we have more data.
Like many posted above, sports is inherently "genetically unfair" and I don't think strongly either way in this particular issue, I just commented because quite a few lay people seem to oversimplify this.
https://pubmed.ncbi.nlm.nih.gov/22561975/
This is just a single study - clearly little - but nevertheless it seems to suggest that differences between prepubescent girls and boys are statistically significant, and confirms some empirical idea that girls are more flexible and have better balance whilst boys are stronger and more explosive.