Constitutionally, I believe this is largely untrue. Non-citizens can't vote or hold federal office, but are otherwise granted the privileges assigned to all people by the remainder of the US Constitution. This likely (IANAL) only applies within the bounds of US borders/territories/holdings, but that's where the FBI should only be operating, IMHO.
The exceptions written to this by Congress (FISA, USA PATRIOT, etc.) are unconstitutional and should be struck down.
One of the differences in the US is that evidence obtained by espionage is rarely admissible in court. Often spying bypasses constitutional and legal protections and renders evidence unusable. In the US, cases get dismissed all the time because evidence was "fruit of the poisonous tree" where law enforcement attained evidence unconstitutionally or illegally. This evidence is not allowed in court. This often renders the work of agencies like the CIA, DIA and NSA fairly useless BUT NOT ALWAYS useless for law enforcement. A lot of the problem with FISA and PATRIOT act is they create loopholes in the line between espionage and law enforcement.
I agree. The ethos of the US is described in the Declaration of Independence.
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."
Our laws, particularly those restricting government power, apply equally to all humans.
The exceptions written to this by Congress (FISA, USA PATRIOT, etc.) are unconstitutional and should be struck down.