Bullsh*t.
They spoke about "and subject to the jurisdiction thereof..." within the context of the of the 14th Amendment. That Amendment begins the the words, "All persons...".
"All persons..." encompasses foreign nationals/immigrants.
Again,Senator Trumball specifically said,
"The provision is, that all persons born in the United States, and subject to the jurisdiction thereof, are citizens. That means subject to the complete jurisdiction thereof. What do we mean by complete jurisdiction thereof? Not owing allegiance to anybody else. That is what it means."
Foreign allegiance on the part of immigrants is something that has always been recognized by our laws and lawmakers. That is precisely why every immigrant that becomes a fully naturalized citizen is legally required to renounce all allegiances to their country of origin and its government as part of their Citizenship oath.