It seems this language is used to emphasize the fact that a person's sex is not something that they can choose, but rather it is a biological characteristic that is named by the doctor at the time of their birth. Additionally, I think this wording can help to avoid confusion or ambiguity, as terms like gender, sex, gender identity are not well-understood by many people.
How can they possibly be well understood when supposed experts use such imprecise terminology? With rampant usage of such imprecise terminology, one can't help but wonder if it is the experts who are confused.
Biological sex does not cease to exist if the doctor fails to identify it at birth. To say biological sex is the characteristic named by the doctor at the time of birth communicates zero information about what biological sex actually
is. Identification by a doctor is neither a necessary nor sufficient criteria of biological sex. It is not a
property of biological sex. Identification by the doctor is a proxy.
By analogy, it is the equivalent of someone asking, "How can you determine a person's blood type?", and answering, "A person's blood type can be determined by asking the person's doctor." It is a technically true answer. But it communicates no useful information, because identification by the doctor is not a
property of what blood type is.
In the gender identity context, people define gender identity in the same manner. People will say gender
is what someone self identifies as, as if self-identification is the fundamental property of gender. Whether this is true or not simply depends on how you define gender, which I take no position on. However, it may be useful for you to confirm whether you believe self-identification is the fundamental property of gender -- or whether self-identification is analogous to the way in which a doctor identifies sex -- a proxy to a more fundamental property.