Yeah, I know what IAAF said. I'll stand by my statements over IAAF's and over that other paper you linked to, though.
The IAAF and that paper relied on information that researchers gleaned from doing computerized searches through the PubMed database for certain terms in abstracts of papers that have been digitized and uploaded to PubMed. That's a good way to begin to research this topic, but it's basically just surface grazing. To get a fuller and deeper picture, you've got to go top research libraries like LoC, NYPL, and New York Academy of Medicine and search deeper and wider, looking for info about the various conditions at issue here in primary sources going back to at least the early 1970s (some of which haven't been digitized). Relevant papers and case reports need to be read in entirety and their footnotes checked too. Telling a computer to go search for X, Y and Z terms just doesn't compare.
Also, some of the most important work on this topic won't show up via PubMed. Such as articles and case reports in NEJM from the 1970s through the 1990s, chapters in various medical textbooks, and lectures, papers, articles and books by people like Milton Diamond and Alice Dreger in places outside the scope of PubMed.
In any case, does it matter whether someone with DSD identifes as male or female?
It doesn't matter to me personally. The whole "identifying as" phenomenon is alien to me. Not just with gender, but with race and other elements of personality too.
However, gender identity matters for convos about XY DSD athletes in women's sports because ever since the Maria Jose Martinez Patino case in the 1980s, the arguments for why XY DSD athletes must/should be included in the female category has largely relied on their gender identities, or rather the claims they make about their supposed gender identities.
Gender identity also matters here because respecting the gender identities, claimed and genuine, of XY DSD athletes like Chand, Semenya et al has caused the virtually everyone involved in or covering these cases to use inaccurate, obfuscating terminology that sows confusion, spreads misinformation and leads to less understanding of XY DSDs - and of female physiology, fitness and sports performance - rather than more.
For example, in the court cases and the press coverage, Chand and Semenya et all have repeatedly been described as "women with high testosterone," "female athletes" and "hyperandrogenic females" - as if though they genuinely were female and have PCOS or LOCAH.
In the Semenya case, the reverence shown to Semenya's supposed gender identity has led to total absurdities such as describing Semenya as "XY female" and pretending that 5-ARD is a DSD in females. When in reality this enzyme deficiency only affects the sex development of males. When it occurs in females, 5-ARD is not a DSD; it has no effect on female development in any way - and no appreciable effects in females over the course of life. Most females go their whole lives unaware they have 5-ARD.
Calling XY DSD athletes like Chand and Semenya female skews research too, and sows further confusion and misinformation about how human female bodies function. Much of the evidence that's billed as being about testosterone and its impact on the sports performance of elite female athletes is really about testosterone and its impact on the sports performance of XY DSD athletes with particular XY DSDs competing in the elite female category. These XY DSD athletes have entirely male physical characteristics - chromosomes, genes, testes, male T levels, male androgen receptors - and as result, findings about them cannot be assumed to be applicable or at all relevant to those who are female.
Female physiology and health is already insufficiently studied and understood. Pretending that research about the bodies of XY DSD people, some of whom can father children, is really research about, or relevant to, the bodies of XX people with normal female development - all of whom have female organs, not testes, prostates, male ARs - does a huge disservice to women and sets back knowledge of how women's bodies work rather than advances it. I don't mean that XY DSD people shouldn't be the subject of medical and scientific research. I just don't think it's helpful to anyone to pretend that research about the anatomy and physiology of XY DSD people is relevant to those of us who are female.