I think, since the assignment is typically done by a medical professional (at least for recording a birth certificate), the assumption is that the gender is either a quickly fixed clerical error or reflective of a phenotype that presents as sufficiently male/female to convince a professional.

"Convincing a professional" is a reasonable proxy for biological sex, given that the cases that would fool a medical professional are in many (most?) cases sufficiently ambiguous that a reasonable person could take either side for what the biological sex is.