Samuel Alito's weird dissent in the Westboro case

Samuel Alito offered the only dissent to today's Supreme Court ruling affirming the right of the Westboro Baptist Church to mount its anti-gay pickets at military funerals. If I read the dissent correctly, he claims the First Amendment didn't protect Westboro's picket of Matthew Snyder's funeral because some of picketing material might've implied that Snyder himself—a private individual—was gay:

Other signs would most naturally have been understood
as suggesting—falsely—that Matthew was gay. Homosexuality was the theme of many of the signs. There were
signs reading “God Hates Fags,” “Semper Fi Fags,” “Fags
Doom Nations,” and “Fag Troops.” Id., at 3781–3787.
Another placard depicted two men engaging in anal intercourse. A reasonable bystander seeing those signs would
have likely concluded that they were meant to suggest
that the deceased was a homosexual.

And later:

In light of this evidence, it is abundantly clear that
respondents, going far beyond commentary on matters of
public concern, specifically attacked Matthew Snyder
because (1) he was a Catholic and (2) he was a member of
the United States military. Both Matthew and petitioner
were private figures,16
and this attack was not speech on a
matter of public concern. While commentary on the Catholic Church or the United States military constitutes
speech on matters of public concern, speech regarding
Matthew Snyder’s purely private conduct does not.

Even if Westboro has the right to demonstrate against Catholicism and the U.S. military, in other words, the church doesn't have a right to cast a false light on a private individual's behavior. Which: So far so good. That's true. But Alito brings his point home in a way that I find confusing:

I fail to see why actionable
speech should be immunized simply because it is interspersed with speech that is protected. The First Amendment allows recovery for defamatory statements that are
interspersed with nondefamatory statements on matters
of public concern, and there is no good reason why respondents’ attack on Matthew Snyder and his family should be
treated differently.

There's one potential problem with this: As I understand it, you can't libel the dead—and you can't defame the dead either. "As a rule, you cannot defame the dead. Under the law, the right to not be defamed is a personal right – only the person in question can sue for defamation. Therefore, a family member cannot bring a claim against you." And Matthew Snyder is, of course, dead.

Is there some sort of right to privacy that private figures retain in death that public figures don't? Because on the face of it, Alito's dissent stretches for a pretty iffy reading of the law in order to justify trampling Westboro's First Amendment rights. What am I missing?