Hmm. In a similar vein, in II, the line "your familiy is still called Corleone". Implying a separate Pentangelli family (hence the second person possesive) but yoked to the Corleone family.

So the Clemenza and Tessio "families" of I and the novel are "families" in the sense of semi-autonomous regimes under the command of the Corleone family.

Or perhaps Puzo is referring to the small-f families (ie blood family) as opposed to the large-F Families (the Crime family)?