https://www.aclu.org/other/constitution-100-mile-border-zone
What you do have is a lot of Americans will defer to LEOs without a second thought.
The government's position is that they do not. The courts have disagreed, especially with respect to using evidence found under such circumstances in criminal cases.
What does worry me is that at the border I have no rights. The usual protections enjoyed by people inside the US don't apply to me. My privacy and dignity at the behest of the whims of whichever border guard I might encounter, and I have zero legal recourse if my rights are violated.
You're right to refuse is still intact but your request to gain entry will almost certainly be denied.
It's a shame that GWB, Condi Rice, Cheney, Tenet, Ashcroft, and Rumsfeld are walking around, on TV, and sitting on boards and none have faced consequences.
Does this mean that it's now sufficient to turn off your phone in the border, and they can't demand to see it?