It is correct, although the tags were not always given out and many are otherwise lost.
From memory the tag would bear a white sticker printed with a bar code, unique watch case number above and 16610LV 93250 below (the latter being the bracelet code).
Yes, genuine green tags are doctored with fake stickers, albeit normally obvious if you are familiar with the real ones.
The maxi dial will be a good indicator that it is an original LV. Only a very small number of classic, black trim 16610LN models will have naughtily but successfully been retro-fitted with the unique type of LV dial.