Grey market with warranty

[liboozers]

Getting ready to pull the trigger and order my first Rolex. I have been looking at for a 116710 and think I found the one I'm gonna buy. Anyways how does the factory warranty work on a watch bought on the grey market (davidsw,takuya,sohais and such)? If the card is dated and even named to someone else but has time left on the warranty does the new buyer still have access to it in case they have an issue. Like mailing it into rsc will they still repair the watch?
Sorry for the new comer question. Big investment and some of these prices grey market can't be beat. Local Tourneau in my mall had v series 116710 without any boxes or paperwork just the watch and at first was asking $8050 for it. When I stepped in the new Rolex section they formed me of a sale 10% off bringing it down to $7245 plus tax. As opposed to $8450 brand new. Now I see on grey market I can get an almost nib for $7245. What is difference besides having my name on the card?