The Litopia website looks really useful for nonfiction writers. I'm glad you linked to it!
As for Right of Publicity, it generally only applies if you are somehow taking away business from a famous person (or their estate), and it usually refers to things like putting a famous person's picture on a t-shirt. So, if a person sold t-shirts with Michael Jackson's picture on it (without getting the Jackson estate's permission), then Michael Jackson's estate could sue because the seller was competing with them on t-shirt sales, and also possibly making it appear that the estate had endorsed the t-shirt, when it had not. (And in fact, the Jackson estate has had a LOT of cease-and-desists and maybe some lawsuits over unauthorized t-shirt sales.)
In a biography, the author is "selling" his or her own ideas, not just a likeness of a famous person. Right of Publicity generally doesn't apply to biographies, unless a biography is so incredibly negative that it causes sales of the subject's products to drop. For example, my Jackson bio is actually quite sympathetic, but if someone wrote a Jackson bio that was so negative it caused some people to stop buying Jackson's music, then the estate could sue over loss of their Right of Publicity.
The radio program in the link discusses a case in which someone used J. R. R. Tolkien as a character in a piece of historical fiction. Tolkien's estate sent a cease-and-desist order claiming that this infringes on their right to use Tolkien as a character in historical fiction. Even though Tolkien's estate hadn't sued (at least not yet), the author of the historical fiction is going to court to try to get a "declarative judgment" saying that he does, indeed, have the right to use Tolkien as a character in historical fiction. The announcers on the radio show say that if the historical fiction writer loses his case, this could theoretically make it impossible to use famous deceased people as characters in historical fiction. And, then they say maybe it would even make it impossible to write unauthorized biographies.
I don't think the author will lose his case (how does his writing a historical fiction stop the Tolkien estate from selling their own historical fiction involving Tolkien? It's not directly competing, like a t-shirt would, because each fiction work has it own ideas.) Even if the author did lose his case, it would likely affect only historical fiction, not biographies, and then only in the state of Texas (where the case is being brought.)
In general, unauthorized biographies enjoy strong First Amendment protection in the US (subject to libel laws, of course.) I don't think that will change anytime soon.