"Choose an Action card in your hand. Play it twice."
Throne Room thinks, "Okay, so the player has chosen this Action card, its name happens to be Band of Misfits (but I don't really care about that), so let's put the card into play and execute it....WHOA OMG SOMETHING WEIRD HAPPENED WHEN I PUT THE CARD INTO PLAY--BUT I DON'T CARE, I'LL JUST EXECUTE IT ANYWAY."
When you Throne Room (or King's Court) an action card, I don't see how Throne Room cares about the NAME of the card it plays twice; it cares about the actual physical card. It told you to choose a card. You did. So there's a card, which is a physical object in the world. The sequence of events is:
1. Throne Room puts the physical card you selected into play.
2. The when-played instructions on the physical card are executed in order.
3. Throne Room puts the physical card you selected into play a second time (although what actually happens is that the card is either already in play or Throne Room has lost track of it, so this fails).
4. The when-played instructions on the physical card are executed in order.
When you put BoM into play, it immediately turns into a different Action card from the Supply. For as long as it remains in play, it is that card. So obviously if you Throne Room a Band of Misfits card, and play that BoM card as a Village, the physical card will be a Village for both plays.
But this is muddy if the card leaves play during the first time it's played by Throne Room. If you Throne Room a BoM and choose for it to be Mining Village, then the BoM card is a Mining Village for the entire time it is in play. But hey, let's say you chose to trash that Mining Village on the first play. So now the physical card that was Throne Roomed is in the trash, and is no longer a Mining Village, it's a BoM!
So I'm curious what makes Throne Room remember that the card it played was a Mining Village.