Have you ever heard somebody say "the box is more nutritious than the cereal inside of it"?
I believe that the man claiming the box was worth more than the rifle was letting you know that the rifle isn't worth anything as a collectable. Just a butchered rifle. A replaced stock and barrel bands, though improving the rifle, will make the rifle just another put together. It will never be of much value to a "1903 Collector", with or without the box. Just my opinion.