This is not true at all. There is no Due Process when you're under the purview of USCIS/INS, CBP and ICE. This why visa holders in good standing can get turned-away at the border or destination airport and sent back immediately, even if they have done nothing wrong or violated the terms of their visa - just on the suspicion or hunch of the immigration officer - and they can extend their reach even after you pass through immigration. There's a reason they're called "constitution-free zones": https://www.aclu.org/know-your-rights-governments-100-mile-b...
This is false, and the ACLU should take this page down. In fact, in the 1970s, the Border Patrol tried to rely on this notional "sphere of influence", and was smacked down by the Supreme Court. Searches concomitant with the Border Search Exemption must have some nexus to an actual, recent border crossing.
This is claimed by DHS and not backed by law or legal precedent in the manner you imply.
ICE and CBP do conduct arrests pertaining to border violations within that 100 mile zone, but they aren't shaking down random passers-by for their iCloud passwords. They do have to follow due process.
I don't have citations because I can't prove a negative.
They could presumably investigate you with much greater power outside of the US where you don't have the same rights. I don't know if they could later use that in court, but that was at least what someone argued regarding Silk Road.
"In any event, even if the FBI had somehow 'hacked' into the SR Server in order to identify its IP address, such an investigative measure would not have run afoul of the Fourth Amendment," Turner wrote. "Because the SR Server was located outside the United States, the Fourth Amendment would not have required a warrant to search the server, whether for its IP address or otherwise."