Shops will often put a bass which has been on display in any box that fits, so I wouldn't worry about the box saying cort on it. Also I doubt that anyone's making fake tanglewoods - it would be a lot more lucrative to put a Martin decal on the headstock.
I have a Tanglewood TRB CE "Rosewood Reserve" acoustic bass. Mine has the full "Tanglewood" text in pearl inlay on the headstock, but I've also seen a later version with the big 'T' logo instead and a few other minor differences, so I doubt that's anything to worry about either.
Tanglewood do change their ranges - the rosewood reserve link on their website is currently broken, so maybe your one is an older one which has been discontinued. Tanglewood acoustic basses are very nice instruments and seem to be priced well below other brands of similar quality I've compared mine to (although I did get mine for £230), so I don't think you've got a knock-off, but I'm sure you can get further info on the tanglewood forum: http://tanglewoodguitars.com/community/