I think your understanding is correct.
族 is hardly ever used by itself, except as the colloquial short form of 暴走族, in which case it is pronounced with a low-high pitch pattern, rather than normal high-low.
Though these things get lost in translation, I would guess the word choice was due to the fact that 家族 ends with it. 家族も族だ is like saying 家族 is one of those things that end with 族 (such as 種族, 部族, 民族, etc.) The listeners can infer by category what he meant without knowing what exactly the word 族 means.