It's not so obvious that we can all agree. Is it ever?

What it comes down to is sloppy writing.

Was Puzo sloppy in meaning that there were five other families and naming only four, or was he sloppy in indicating that there were five other families when he only meant there to be four?

Since there's only the one occasion when he has the opportunity to name the family and doesn't vs. all the times that he indicates their existence, I believe that he meant there to be five families in addition to the Corleones.

My logic, to copy and paste, is that since there actually were (and are) five NY families, by including the Corleones as one of the five, Puzo & Coppolla felt that they would be inviting too much comparison and speculation as to which of the five the Corleone family was meant to represent. Since the Corleones were the main characters, I believe that would have been the case. No one would have cared, for example, who Cuneo or Stracci was supposed to be modeled after, but everyone would have been trying to figure out which family head Don Corleone was supposed to be.

But Don Corleone was not supposed to resemble anybody. I believe was the head of a fictional 6th family, whose story was told against the historical framework of NYC organized crime and the five NYC families in the early 1940s, and, as such, he was not meant to be any of those family heads.

We've had many discussions in the past about which of the original Dons Vito Corleone was modeled after, and we've agreed, I think, that he has a few few of the characteristics and personality traits of several different ones.

It was not so much that Puzo was hesitant to have Don C. compared to one of the NYC Dons. It was that he couldn't be compared to any of them.