Based on your reasoning, many fictional characters wouldn't possess their abilities outside of their respective series. For instance, Haseo from Dot Hack or Kirito from SAO wouldn't have their PC body. Amrita is exclusive to Ni-Oh and doesn't exist beyond that universe. Moreover, many fictional worlds have their own specific rules regarding the use of powers such as Force, Ki, Nen, Haki, Chakra, Magic, etc. Therefore, characters from those series wouldn't have access to these powers outside of their respective universes. For example, the characters from FFVII wouldn't be able to cast Magic with their Materia without the Lifestream or The Void.