Of the past ten senators appointed by a governor when a seat became vacant between elections, three indisputably got the job because of their names -- that is, through nepotism.... The most egregious was Lisa Murkowski, Republican of Alaska, who was appointed by her father to fill the seat that he himself vacated when he was elected as governor. Jean Carnahan, Democrat of Missouri, was appointed to the seat won posthumously by her husband after he died in a plane crash. (The governor had promised to appoint Jean Carnahan to the seat if her husband won, so you could say she was really elected, not appointed -- but you could not credibly say that she didn't get the job because of her husband.) And Lincoln Chafee, Republican of Rhode Island, was appointed to a seat vacated by the death of his father.
As Noam noted, Kinsley rather undercuts his case by allowing that Chafee and Murkowski (unlike Kennedy) had both been elected to public office and Carnahan (also unlike Kennedy) was in some respect "on the ballot" when her husband won posthumously. But the more straightforward difference is that in all those cases--and political nepotism generally--an office was passed to a family member of the person who had held it previously, not to a member of some other political family altogether.
Teddy Kennedy, for instance, has reportedly sent signals that he'd like his wife Vicki to inherit his seat--an example of your run-of-the-mill political nepotism (though one that I imagine may be threatened somewhat if Caroline Kennedy gets the New York Senate seat). Now, I don't approve of this type of arrangement at all, but there is a tenuous logic to it, at least for some voters. Specifically, if I voted for candidate X, and he had to leave office for some reason, who is the closest replacement who could be appointed, the person most likely to carry on his work? Well, an intuitive answer is: his wife, his daughter, or his son. (Hence: Carnahan, Murkowski, Chafee.) Again, I think this is silly, but the long litany of wives and children who've been elected to offices formerly held by their husbands and (usually) fathers suggests many voters disagree with me.
Caroline Kennedy, by contrast, wouldn't be carrying on the work of the woman whom New Yorkers elected to the Senate--heck, she didn't even support her in the primaries. So unless some cross-state swap can be arranged in which Teddy offers his seat to Bill or Chelsea, the logic Kinsley invokes really doesn't apply at all.