Earlier quoted context omitted.
That doesn't really make "female DNA" a thing, because XX vs. XY does not tell us enough to know for sure if someone is male or female in the sense that the words are normally used. There are natural XY females who have a mutation in the SRY gene, XX males who randomly got a functional SRY on one of their X chromosomes, and other XY people whose bodies can't process testosterone and thus are female in almost every re…
There's are days during the year when the sun doesn't set at all around the arctic circle. No one would argue with the statemet "the sun sets at night". More directly, there being extremely rare exceptions to a general rule doesn't make the rule false. There's a reason the phrase "the exception that proves the rule" exists.
The actual changes needed to flip an embryo from male to female are fairly tiny. On the other hand, the number of genes related to sex characteristics is large, but they're mostly shared between both sexes and not uniformly expressed in members of a given sex (hence why transgender HRT administered before puberty results in development largely indistinguishable from a natural puberty). So proposing "female DNA" as a cause for some observation seems unenlightening to me.