Bellei's father never resided in the US, plus, that should be irrelevant as it wasn't Bellei's father's citizenship that (in combination with the 1952 Act) produced Bellei's US citizenship. At the time of the 1790 act, the only parent who could transmit citizenship was the father, which is why no act until 1934 would have been of any use to Bellei.
All that said, there is no way to predict how any given individual will come to the conclusion that born abroad is alien, unless a statute covers the person. I think the constitution (14th amendment) plus Bellei, plus Wong Kim ark is the most direct route. Bellei notes the 1790 Act, but doesn't spend much time dissecting it, and doesn't appear to need to dissect it. SCOTUS, in 1971, said that a person born abroad is, if a citizen, a naturalized citizen. If that person was not a naturalized citizen, they could not be denaturalized, and expatriation follows a totally different line of cases.
But, other people obsess over the 1790 statute, and see it as a definition rather than a vehicle for creating a legal fiction of citizenship even though born an alien.
The plaintiff, complainant, objector doesn't get to see the opponents arguments in advance, and the usual process allows the plaintiff a rebuttal to the defendant. Funny thing in these cases is that the defendant (Cruz) never addresses the complaint head on - he make arguments along totally different lines.
Do you have links to the Cruz briefs? I haven’t done a search for them yet to see if they are available to the public at large.