For the purposes of NSA surveillance, the U.S. is like the rest of the world; if you are legally inside the U.S., Fourth Amendment protections apply without regard to citizenship.
If you've so much as ever applied for a green card, you are now a "U.S. person" as far as NSA is concerned.
U.S. treatment of non-citizens outside of the U.S. is different in some (not all) ways, that much is true. But other countries take that tack as well. E.g. even privacy-friendly Germany allows their foreign intel agency, BND, to spy on the communications of non-Germans.
in general terms, in most places, the law is applies equally to everyone in the country[+].
in contrast, in the usa, many things apparently depend on whether you are a citizen or not.
those are quite different approaches. both can be made to work (neither "falls apart"). the american one appears arbitrary and unfair to me.
[+] obviously there are exceptions - immigration, for example.