I like this post, becuase it raises an important point. As you note, a player's nationality does not always tell you they developed their game or where they first built their championship level skills.
Hence, I agree 100% that Mika should be thought of as American, for most of his development as a player came in America playing American events.
Appleton, though he has moved to America recently, is a product of the English 8-ball system and the Euro-tour. Hence, I'll always think of him as European.
Hohmann was already a World 9-ball champion when he moved here. He is a product of European competition and European coaching and instruction.
I'll always view Pagulayan as Fillipino, for all of his influences are Fillipino, he is a product of the Fillipino system, and plays the Fillipino style of pool.
Certainly, everybody on this year's Team Europe is European in the sense suggested here. Like you, I'd like to see Pagulayan added to "Team North America," assuming he is a dual citizen of Canada and the Philippines.
Your post reminds me of when Martina Navratilova played for the US Federation Cup team (ladies equivalent of the Davis Cup team). Sometimes, nationality, competitive origin, and residence can obscure the picture of international pedigree.
Thanks for your insights.