Hard to say. Not saying that you’re wrong, as I’m personally agnostic/on the fence about Giunta’s official status. Chicago had its last two bosses murdered in the space of a few months, so I’m honestly unsure that politically they’d be in the position of being able to formally elect or ratify a boss. Several scenarios could be consistent with what we know about Giunta: he could have been formally installed as rappresentante, he could have been acting as capo of the Family but never officially held the title, or he could have attempted to seize the office and died trying. If the Family was at war with itself following the LoLordo hit, then we have reason to suspect that they may not have been able to install an official rappresentante that would be recognized by the national organization.
With respect to the notion of puppet bosses, maybe this accurately described the relationship between Capone and men like LoLordo and LoVerde. Or, alternatively, they were more like partners with common aims and interests (at least up to a point; LoVerde’s interests apparently led to him bleeding out in the floor of a vacant social club, though there remains much that we don’t understand with what happened with after Capone became official boss). Gentile understood Capone to have been the “real capo” of Chicago despite being still formally a Masseria capodecina, but framing LoVerde as a puppet, for example, I think may be somewhat overstated.
As with most of these events, there were competing narratives and claims put out by several sources. The Chicago Tribune claimed to have it on good authority that Giunta, Scalise, and Anselmi were sacrificed by Capone as part of an effort to secure peace in Chicago at another meeting allegedly held in the Spring of 1929 in Cleveland. The claim was that Aiello leveled charges against these three men for having violated a prior pact and that the meeting ruled against them, with Capone being powerless to overturn the verdict. Not saying that I think thats’s what happened, but we don’t have a Nick Gentile in this case to provide an insider source, and these things often played out very differently behind the scenes then we would guess. The press was often plain wrong and even dishonest, but they also sometimes had sources actually in the know.
You’re probably aware that the Tribune also reported that sources alleged that it was Aiello who dropped the dime on the Statler meeting to CPD.