There's Supreme Court precedent establishing that this isn't the case. ACLU itself had backed off it, last I checked, but since they used it for a very long time in fundraising, people will never, ever stop believing that 80% of the United States lives in a "Constitution-free zone". You cannot in fact be border-searched on the streets of Chicago; in fact, you can't even be border-searched at a lawful fixed immigration checkpoint.

Border searches need a nexus to an actual border crossing.