She means that "sex" refers to the physical nature of the baby (male or female). In some (academic) circles, "gender" refers (only) to the cultural acclimatization of the person in question, or to that person's sense of him- or herself (so a person with XY chromosomes who felt like a woman would be of the male sex, but female gender). Merriam-Webster, however, considers the two words synonyms. Her distinction is thus incorrect (at least in the world at large).
Talk de jour, are you a member of this DDC?
Here's the main entry for gender:
Main Entry: 1gen·der Pronunciation Guide
Inflected Form(s): -s
Etymology: Middle English gendre, from Middle French gendre, genre, from Latin gener-, genus birth, race, kind, class -- more at KIN
1 a archaic : KIND, SORT b : SEX <black divinities of the feminine gender -- Charles Dickens>
2 linguistics a : any of two or more subclasses within a grammatical class of a language (such as noun, pronoun, adjective, verb) that are partly arbitrary but also partly based on distinguishable characteristics such as shape, social rank, manner of existence (as animate or inanimate), or sex (as masculine, feminine, or neuter) and that determine agreement with and selection of other words or grammatical forms <Latin has three genders, masculine, feminine, and neuter> <French has two genders, masculine and feminine> b : membership of a word or a grammatical form in such a subclass <a Latin noun has gender, number, and case> <an English noun has, strictly speaking, no gender> c : an inflectional form showing membership in such a subclass <a Latin adjective agrees in gender with the noun it modifies>
Citation format for this entry:
"gender." Webster's Third New International Dictionary, Unabridged. Merriam-Webster, 2002. http://unabridged.merriam-webster.com
(27 Aug. 2007).
And here's a secondary entry, not included in the main definition:
Main Entry: gender Pronunciation Guide
: the behavioral, cultural, or psychological traits typically associated with one sex