Certain types of searches are assumed to be reasonable when passing through a border. It's not that the fourth amendment is suspended, but that "reasonableness" is context-dependent. Some types of stops are allowed near the border (CBP border checkpoints, that sort of thing). That's what the "100 mile" thing is about.

Even people held at Guantanamo Bay have some limited Constitutional rights, specifically habeas corpus rights[1]. You would have noticed if habeas corpus had been suspended 100 miles from the border (it hasn't) or if first amendment rights had (they haven't).

The argument the ACLU is making in this lawsuit is that the sorts of searches that are allowed at the border (checking for contraband, etc) do not cover the sort of searches actually being done (general law enforcement). The border search exception is intentionally narrow: it's to check if people are smuggling rare birds down their pants, not to trawl for general evidence of criminality. Hence the lawsuit.

[1] https://en.wikipedia.org/wiki/Boumediene_v._Bush "The Constitution grants Congress and the President the power to acquire, dispose of, and govern territory, not the power to decide when and where its terms apply. To hold that the political branches may switch the Constitution on or off at will would lead to a regime in which they, not this Court, say 'what the law is'."