I agree that "any given country" sounds better than "any country" in Navi's examples.
As to agreement of subject and verb in (4), I was taught in elementary school that when two or more subjects are joined by the conjunction "or", the number of the last subject determines the number of the verb. I have since learned that much of what I was taught in elementary school was wrong, but I have seen this rule confirmed since then.
It would seem on the surface, then, that the verb should agree with "a majority of people" rather than "everyone", and I think there are differing opinions as to whether "a majority of people" takes a singular or plural verb.
However, would you say that the rule doesn't apply here because "or even a majority of people" is set off as a parenthetical? (And perhaps also because of the word "even"?)