Buying from a grey

[Coopercitygator]

Hi! Pretty new here. Looking to add my first Rolex to my small collection. I did have an Explorer I many years ago, but thought it was too small and sold it.
Anyway, question is this- so, i found the watch i want from a very reputable on this board grey dealer- the watch is brand new. I was told the warranty would be from Rolex and be in my name, and that all i have to do is take the warranty card to an AD and they would swipe and all would be good.
How does this work? Does this make sense? I was always under the impression that an AD would be upset that i have a new Rolex from a grey dealer...and this might cause a problem.
If anyone has any input it would be appreciated. First time having to deal with this, as my current watch is a Breitling GMT-not that hard to come by!
Thanks-