I've watched this clip more than is probably healthy in the past 15 minutes and for the life of me I can't say for certain whether she's joking or being sincere (welcome to the world of watching the royal watchers!)—but that's probably only because I don't want to live in a world where this type of "expert" analysis gets airtime on one of the nation's largest news outlets. Take a look and decide for yourself, and while you're at it let me know your thoughts at @JoshVoorhees or in the Comment section below.
That quote again from Victoria Arbiter, whose father was a press secretary for the queen: "My first thought, I have to say, was this is how brilliant a royal Kate is. There are women throughout British royal family history that have panicked over not being able to deliver a boy, and here we are, Kate did it first time."
For those of you who have forgotten your high-school biology classes, it's the male who technically determines the sex of a baby thanks to the fact that he's the only one who can contribute a Y chromosome. But, then again, it's the women who've historically been blamed (and by "blamed" I mean "beheaded") for failing to produce a male heir, so there's a chance that Arbiter was just having a little fun. Let's hope so.
Update at 5:45 p.m.: Arbiter says it was a tongue-in-cheek joke based on the "shocking" royal history.