The Constitution follows the flag.
I think in the sense that the rights are human rights, then all humans should get them. But the civil rights in the US Constitution and amendments are, for the most part, meant to protect citizens from the government becoming too powerful and abusing its power. The framers of the constitution, being in the novel position of actually getting to decide what the powers of their own government were to be, were very fearful that it would be too powerful. A fear soon validated by the French Revolution's problems. (The idea that civil rights are somehow "earned" as mentioned in this comment thread is odd... the rights are not a "reward" to be earned, they were put in place as a precursor to any government: no American starts off without them and you do not need to be a taxpayer or even a citizen to enjoy them, you just need to be in US-ruled territory.)
It does not make sense for anyone not residing in the US to be given freedom of speech or the right to bear arms by the US government. These rights are allowed (or not) by whoever governs the place where you are. If the US government is spying on you on your territory, it is up to your government to protect you. Note how the US government reacts when another country is spying on our citizens (well, corporates anyway.)
The fourth amendment was not put in place because "gentlemen do not read each others' mail" but because the Brits used to bust in with general warrants to try and collect taxes and it pissed off the colonists. It was not the principal of the thing, really, but the consequences that got the colonists' goat. Since the US government can't really do anything to people not within the US except as an act of war, their search of your property--while reprehensible--is not meant to have been protected under the 4th.
It does, unfortunately, make perfect sense for any non-American to want their Internet traffic kept from traversing US soil if by so doing it places that communication under US scrutiny. I suspect it would not be hard to set up routing tables that keeps traffic from entering the US unless that's the destination (but I'm talking out of my armpit, I'm not a network engineer.)