The issue is clearly not with displacement, but with the UV mapping, which is why adding UV map modifier fixed it. If for some reason you can't use UV map modifier, then maybe UVW xform modifier would suit you better? Contrary to the former it doesn't replace the mapping, but lets you modify already existing one. In your case you would need to change U tile from 1,0 to -1,0 to invert mapping on U axis. If you can't or don't want to use modifiers, you can do the same in the bitmap, that would be -1,0 U tiling in Corona or standard bitmap. Mind you that you would have to do this in all the bitmap nodes that are assigned to that object, so it's less convenient than modifier option.
