As a Brit, I don’t think I’ve ever noticed them 'Hamming it up' in front of Americans, or the Japanese or Koreans, but perhaps I just don’t notice it. And from what I’ve seen on TV shows, Gordon Ramsey seems to be as rude and pompous, or as polite and respectful to anyone who deserves it; no matter their country of origin.
As for calling Japan and (South) Korea 'American Vassal States', I imagine both countries may take issue with that rather derogatory statement, unless the term 'Vassal state' has diminished somewhat from it’s original meaning. Japan and South Korea certainly don’t have limited autonomy, and I am not too sure they are obligated to provide military support, resources, or tribute to their 'overlord'.
Anyhoo, this is not the place for political debate - I’m off to find another Fallow content I may have missed