This is one of the weirdest things. Mainland Chinese need an exit permit to Taiwan and an entry permit from Taiwan to visit Taiwan. However, that permit does not allow them to go elsewhere. When a passenger presents the BP and the permit to immigration, they have no idea that passenger is traveling beyond Taiwan until he/she returns. The passenger may not necessarily return via Taiwan. So he/she may exit on one travel document and return on another. I don't know how that works. Now I understand - they are not supposed to go to a third place.