Hi, lazer.
If I had Moderator powers here, I would break out this or your other post into its own new thread for the convenience of one and all.

Your analysis is reasonable. At least so far as your GGF was concerned, he did not gain citizenship through his father and thus he was applying on his own. However, there are any number of problems with this:
1) it is possible that his father did naturalize prior to June 14/June 30, 1912 (there is some disagreement over the true effective date of the law), and your GGF simply was not aware or was not aware that it would have affected him as well. He filed papers on his own not realizing that he already gained citizenship.
2) GGF may have fibbed when completing the draft card and responding to census-taker's questions in 1920. There was a lot of fibbing going on at a time when proof was not required to be presented.
3) regardless, the consulate will want to see a great deal more evidence regarding naturalization status. In particular, although supporting documents like the census are desirable, they are considered just that - supporting documents. You will still need the all important "No Records Found" letters from multiple sources. This is especially true because, from what we have seen, the Italian Ministry of the Interior has been really cracking down on the naturalization aspect of jure sanguinis applications in recent years.
Due to the timing of events related to your GGGF and GGF, you will need to separately prove the naturalization status of each of them.
* you will need to prove that GGGF did not naturalize prior to either June 14/June 30, 1912, or GGF's 18th birthday, or GGF's "date of emancipation", whichever came first. Date of emancipation refers to the date that GGF began acting in an adult capacity; the details may be argued, but things like taking a wife and moving out of the family home or joining the military might apply.
* you will also need to prove that GGF did not naturalize on his own prior to the birth of his own child, presumably your GF.
In each case, proof consists of locating an actual naturalization document - a naturalization certificate or a signed Oath of Allegiance (which actually appeared on the backside of the Petition for Naturalization document). If no such document can be found, then suitable letters stating that fact are required from, at a minimum, the USCIS, the National Archives, and the state and county courts covering every jurisdiction in which the person was known to have resided in the years of concern. Remember, these requirements will apply separately to both your GGGF and your GGF.