This is the standard silliness as the right tries to find some way to defeat birth citizenship.
There are numerous contemporaneous statements that contradict Trumbull. The US has always recognized the citizenship of children born in the states.
Won Kim Ark is the case law. Which makes it clear WKA is a citizen even though his parents were far more objectionable than illegal aliens. They were barred by statute from citizenship and they and their son were clearly subject to the jurisdiction of China.
The simple fact is the newborn are all citizens except the children of foreign diplomats and soldiers.
the only interesting argument is the one about the Indians…but then you get into the question of whether a tribal area of the Indians is in the United States. Pretty good case that they were not born in the states. The US and the Indian lands may actually be co-located…but they are not the same place legally.