I was going to post that it was more of an editing error than a fact error.
And remember, the topic wasn't why the borough is called the "Bronx", but why it's called "the" Bronx, when no other borough gets a definite (or indeed any) article.
I think Frazier was trying to use this, rather artificially, as a hook for describing some of the major differences between the Bronx and the other boroughs. Because none of the facts he raised could account for the article.
I don't think it's knowable why the Bronx gets a definite article. ("Bronx County" of course receives no article.)