It is extremely confusing to equate Immigration and Customs, even though both are administered by Customs & Border Patrol (CBP). Indeed CBP runs an International-to-International (I-T-I) program at DFW, MIA, and IAH for checked luggage which is specially marked with an ITI tag.

This has nothing to do with Immigration or with Customs for carry-on luggage. The bottom line is that there is no such thing as "transit" in the US and has not been since the 1990's. There are some limited physical arrangements such as the NZ arrangement with CBP at LAX, but that is not relevant to this thread and deals only with a unique physical gate situation. It is simply a decision by CBP not to inspect passengers who remain penned in a specific gate.

If you are deemed inadmissible to the US, you would either be returned to the country from which your flight originated, your country of citizenship or residence, or a country which the US is assured will accept you. If your inadmissibility is due to the failure of documents, the financial responsibility for your return befalls the carrier that brought you to the US. If you are properly documented but otherwise deemed inadmissible, the financial responsibility befalls the US.

I know of at least two people who have been deemed inadmissible, but who have been permitted to continue their onward journey after the onward destination country advised CBP that they would be admitted on arrival. CBP gave them the choice to be returned to their origin or to be escorted to their onward gate. They gladly chose the latter and were discretely escorted by an Officer to their departure gate.