In particular, the Supreme Court of the US gets to vote on what the Constitution means. And that sometimes yields non-intuitive interpretations of the plainly apparent reading of the rights amendments.
For instance, the 4th Amendment would seem to indicate that the US cannot spy on foreigners without a warrant. Only two justices had the stones to confirm that. The majority voted that interpreting the amendment as written would make it too difficult for the US to gather foreign intelligence. They literally voted that extending basic human rights to everyone would be too inconvenient.
It doesn't matter if the original intent was to protect everybody, rather than just citizens, when those tasked with judging cases may be swayed by political expedience.
It is my opinion that reading the US Constitution should be sufficient to understand the entire foundation of US law, rather than also being forced to study several centuries of judicial precedent under Anglo-American Common Law. As an American, I want the US government to get a warrant before conducting a search, on anyone, anywhere. I don't particularly care whether they are citizens, because I don't want the US agent to be an asshole when supposedly representing and defending my interests.