So why does the EFF say that it does apply?
https://en.wikipedia.org/wiki/Border_search_exception
Here, the EFF has to show that the search that was conducted wasn't reasonable in some manner or that it otherwise violates due process. They will need to show that the execution of the search wasn't reasonable, because being subject to a search in and of itself generally is. The only SCotUS ruling on search of electronic devices has been Riley v California (https://en.wikipedia.org/wiki/Riley_v._California) where they ruled that a search warrant was required to search an electronic device even when an individual has already been placed under arrest.
The EFF disagrees. You can read their reasoning in the linked article.
It's a way government can eschew all constitutional protection for private data, by simply waiting for the target to cross a border, practical for a majority of citizens. Data is substantially different from physical possessions because it's very portable and most people do indeed carry vast amounts with them when traveling.
Furthermore, in the modern world data import or export offenses (espionage) do not employ physical border crossings, so there is almost no reasonable offense the search could uncover.