No, what's beside the point is the initial origin of these values. The key point, the germane point, is that origin of the value system is not relevant to the current situation because the phrase "it's an American thing" is referring to the present or recent past. It is not referring to the reality a century or more ago. America is, clearly, the dominant cultural force in the West as well as the main driver behind these values. You can find plenty of academic research to back that up as well, shockingly enough other people also attended college and covered cultural studies, media and communications. Which is probably why so many of them have time to waste on internet message boards
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Was it originally a British thing? Certainly. No-one's contesting it's origin. But it is most certainly "an American thing" these days.