Well, we don't actually know that for certain: it's plausible that trans people are at least in some cases the result of abnormal development of sexually dimorphic brain architecture that supports synergy between the sex of the body and the model of the sex of the body in the brain. This is neither something with strong evidence in favor, nor strong evidence against, but given DSD phenotypes ought not be ruled out a priori. However, the article didn't try to make that link, so I agree that having both topics in there without commentary about the link or lack thereof was potentially misleading.

Anyway, the problem with your perspective is that it simply isn't the case that there is a single regulatory mechanism that is responsible for sexual dimorphism--not even at the cellular level, much less the organismal level.

Now, I completely agree that the regulatory feedback that exists does, insofar as we know (and we know a good deal), involve two alternative feedback loops with switch-like behavior, where we call one state of the switch "male" and the other "female". The problem is that given the distributed nature of genetic regulation, when the feedback is broken in some way, there is not any unambiguous principled way to label what case you're in any longer. You can pick something arbitrarily, but the choice of what to pick is arbitrary.

When studying sexual differentiation pathways, nobody has any particular confusion about this: you simply state what is going on, possibly because you intervened. For example, in Drosophila, the state of Sexlethal (sxl) splicing is determined by X dosage (probably more absolute than X-to-autosome ratio), with no real "default" because the number of chromosomes you normally get is binary (1 or 2). Sxl has an autoregulatory feedback loop to maintain the original decision, which is immediately picked up by the two transformer proteins (tra and tra2) which in the absence of regulation have male-specific splicing and when regulated by sxl have female-specific splicing. These then go on to signal to doublesex (dsx) and fruitless (fru) which have their own male and female specific isoforms and each handle part of the job of sexual differentiation (doublesex is body, fruitless is brain, approximately, though dsx has some impact on behavior also).

But wait! That's just somatic sex! Germline sex is determined by a different mechanism involving ovo-A and ovo-B!

So you can end up with pretty much everything you can think of: fly with male body and male behavior and a male somatic gonad trying and failing to make sperm because the germline thinks its female and gets really confused when the somatic gonad says "hey, sperm!" and internal signals say "no, egg!". Even if you're super gonad-centric, this is confusing--and anyway, in every other way the fly is exactly male, so it seems really weird to say that despite almost all the regulation pointing in the male direction, that the germ cells got confused and died instead of turning into sperm means that the organism "is female". I mean--you could do that. But it's not an objective choice at that point.

I pick flies because this is all really well worked out compared to other systems. We can do almost anything we want. There are conventions that tend to be followed (e.g. if you switch the somatic sex determination pathway, it's common to say the fly "is male" if the somatic morphology is male and "is female" if female), but really, you broke the system that has two endpoints. You now have a mess. You can make any kind of mess you want, too, which is maximally confusing for any single "train has two endpoints"-type reasoning.

Now, it is the case that there are a lot of "intersex" conditions in humans where any sort of reasonable classification would say "that's female, just not completely normal", or "that's male, just not completely normal". But there are others where either you just have weird stuff happening (e.g. all the chromosomal ones--you generally have characteristic misregulation where you get consistent phenotypes that are neither male nor female, which doesn't mean it's "another sex" but it does mean "if you view this as a train with two endpoints you're gonna be confused"), or you really do have intermediate phenotypes (so "intersex" is a very apt descriptor). And we haven't even gotten into mosaicism, where the cell-to-cell decisions about sexual differentiation don't even match. Anyway: third sex, no, there's no third station for the train to stop at. Intersex, yes, sometimes the train ends up between the two stations. Binary: when it comes to properly-working regulatory processes yes; when it comes to everything that can and does go wrong, not hardly, the train can derail in all sorts of weird ways, including falling apart and sending different bits to different places.

Anyway, the point is: because the regulatory process is distributed across a variety of genes, there is no universal source of truth to which you can appeal. You can force it by making a decision that handles every possible way in which the usual coregulation can be broken, but that's not a statement of discerning a clear regularity in the universe from which many things follow.