ICE acts outside of the law anyways, so whatever the law says or doesn't say seems to have no real impact on how they behave. The article itself mentions only searches at the border when entering the US, so this legal precedent (in theory) shouldn't enable them to perform a warrantless search if you're already in the US.
If you have more legal context than the author and want to read further into the precedent than that, I'm not here to say anyone is wrong, just that the scenario you mention doesn't seem to apply to what the article is describing.
The border search exception allows warrantless searches of persons or property crossing the U.S. border, including the functional equivalent of the border such as international airports