Kim, I think you're absolutely correct that some people are using "a broader definition". Sometimes it includes chromosomes and anatomy; I've also seen it used to include hormone levels (as noted in the main article).
The problem is, if you use an overbroad definition of a word, the word ceases to be useful; it ceases to have the predictive power that you want from a word. Defining "biological sex" as "all sorts of genotypical [genes/chromosomes] and phenotypical [what the body looks like] expression" adds a layer of complication onto the simpler definition of "biological sex". There are already more complex descriptions (eg "phenotype") of how our physiology is overlaid onto our biological sex.
Some people don't like that: it seems as though scientists are just making things more complicated by having words like "genotype" and "phenotype" when they could just say "sex". But science is about precision, and layering levels of precision on top of one another, so that the entire edifice is solid, and you can make predictions about the world. If you start from weak foundations - eg saying "sex is defined by your chromosomes and anatomy and hormones, in some mixture" - then you soon run into problems because you can't predict outcomes: if a 46 XY DSD person tries to procreate, will they succeed if they pair up with a 46 XY person? You can probably figure out that the answer is "no", because that's how biological sex works, but going by "well, 46 XY DSD is on the spectrum towards female, so maybe?" will always give the wrong answer. One definition of "sex" always gives you the correct prediction; another never will. So you want to use the definition that gives you the correct answer to a possible situation. That's how science works.
Thanks for the response - it's a worthwhile question to ask.