Thanks for the extensive answers everybody. Your cops still have way less authority than the cops over here in my neck of the woods.
So, going off of what Albatross said... if I was an J-1 Visa holder (foreign exchange student in the States), in which is said that that I am not allowed to sit in a car with anybody except for my legal guardian over there or a person from the school to which I go. If I was caught by a cop doing such a thing, could they detain me for having a reasonable suspicion (having a funny Slavic accent, not looking like I am from the area, etc.) could they ask me for my citizenship or for my passport and VISA?