Except that is completely false.
How many foreigners are currently in US jails? If there is more than zero then clearly they are subject to US jurisdiction.
I'll give you a hint, there are a lot more than ten thousand in US jails. If the USSC rules that they are not subject to US jurisdiction then the US would be jailing them illegally. Not only would they be immediately freed, they could sue the government for hundreds of millions if not billions for being illegally held in violation of US law and the US Constitution. Treaties allow for foreigners to sue the US government.
Why do you think the US used Guantanamo for holding Al Qaeda members? It was to prevent them from being subject to US jurisdiction if they were being held inside the US.
Everyone on US soil other than foreign diplomats are subject to US jurisdiction. No sane court will rule otherwise because the consequences would be catastrophic for the US.