[dragonwriter]

> It's been 30 years since I've studied formal writing in earnest, but "they," is, or at least was, grammatically incorrect in that sentence, unless you are referring to more than one person.

It is incorrect, as is “her” both times used in the preceding sentence, but not because of number of the referent (a sibling comment addresses “they” and its long-established singular use, but that's not actually relevant here.) Rather, “her” is incorrect because the possessive pronoun that corresponds to the “one” used in the earlier clause of the same sentence and with which “her” shares a referent is “one’s”, not “her”. And “she” is incorrect because it has, again, the same referent as the subject pronoun “one” in the preceding sentence, and therefore should use the same subject pronoun.

> English doesn't have a proper gender neutral singular pronoun.

Leaving aside whether it does for a known, specific referent, it absolutely does for an generic referent, and it was even properly used in one of four places the same generic referent was referred to using a pronoun in the last two sentences of the post: “one (subject)/one (object)/one’s (possessive)”.