I have two Rolex's, no Submariner, an explorer and Daytona. Both had wooden boxes covered in leather and with a padded interior. No plastic except the tags, so I would suspect this is not an original box.
I bought a none date Sub from a well known high street AD, brand new and my box is a green plastic one (comes inside cardboard box). This is the last model (i.e. not the new one) and I bought it in July 2008.
So as far as I'm concerned all is present and correct.
I bought my wife a 2005 Rolex, not a sub but a womens model and that came in a plastic box (with a wavy top design) inside a cardboard box, as stated previosly, so all seems correct.