This is a tricky one for me. Warrantless searches aren't illegal depending on what's being searched. For a quick example -- the cops can look through your back window into your car without a warrant, it's a warrantless government search. But they can't make you pop your trunk without a warrant. Or the common domestic understanding is that anything a random person can buy off the street can be used by the government and things they learn through these methods are not illegally obtained (that's a very broad explanation, lots of nuance and detail).
The problem in the modern era is just how much information people have turned over to non-government entities and those entities are entitled to use or share that information as they wish. Moreover, US laws, such as the 4th Amendment don't apply overseas because our laws end at our borders.
This puts us in a tough place. The government can search anyone overseas without a warrant but if Americans are sharing information with those overseas individuals then the information obtained from the overseas individual is legally obtained, even if it includes information about the American. As the article points out, once the government builds a database with this legally obtained information, it's no longer our private info, it's theirs and they can search it without violating the 4th Amendment.
I suspect that this is an irreversible outcome, regardless of the gnashing of teeth. The world of information is global now and that means that government protections we take for granted don't have the same teeth that they did 200+ years ago.
The legitimate only real solution would be a one world government but that, obviously, is not going to happen anytime soon. So people have to be smarter about their own actions knowing that nothing we do via phone or internet is hidden from the government.