So is it a fallback of sorts, or did it infringe upon another tileset in the memory?
Try changing the base tileset to one of the same size and see if it also uses White.bmp.
it actually depends on whatever was loaded into the memory previously. Imagine the space for tilesets as a 256x256 square - new loaded tilesets are placed over the top-left corner. white.bmp is a fairly large tileset, and it's loaded during the intro (u_kings) so naturally if you pick a tile out of bounds it's likely to come out of that.
So if you transport the player to a diferent map with a different tileset, and then transport back, you can use the tiles from the second map in the first map for a cutscene?