Source?
Also, the supreme court has ruled that asking for ID at stops is constitutional.
https://en.wikipedia.org/wiki/Hiibel_v._Sixth_Judicial_Distr...
>asking for ID
The same supreme court ruling you named stated the reason why they could even demand ID was because there was no expectation it would implicate them in a crime. Demanding immigration papers in an immigration investigation would reasonably be asking someone to incriminate themselves if not having them is an element of that crime (for the same reason, if a minor is stopped for say having booze, generally they are not required to give DOB even if the stop-and-ID statute requires it).
The bit you are interested in googling is "general warrants" as one of the things colonists were quite angry about.