Is the OD of the new and old tube the same? The one with an ID of 1.004" obviously isn't a 1" OD steerer.
I've had 1" steerers that are different wall thicknes on threaded tubes. How common that is for threadless steerer tubes, I don't know. Assuming the star nut was bought for the correct OD size I'd think it'd push down into and work with tubes of differing wall thickness. However once used with a thick wall, it likely won't hold in a thin wall.
Perhaps you got a returned star nut from someone that shoved it through a tube already.