Then, they are an American Team that play in Bermuda.
No, they're Bermudan team that chose to play in the US. Unlike Europe, sports in the US is just business, and league is a business too, and any club is just a franchise. It doesn't matter if they are based in the US, Canada or Mars. That's what Europeans don't undeerstand is that in NA the leagues are multinational by definition, as all of them have Canadian clubs. According to you, NHL should be a Canadian (or American?) league, and NBA is purely American?
BTW, Hogges do NOT qualify for any other US Competitions like US Open Cup.
I think Swansea or Cradiff should NOT be considered an English club, rather Welsh clubs playing in English league.