An excerpt from this onemileatatime trip report- http://onemileatatime.boardingarea.com/2015/08/30/ek17-to-manchester-having-the-best-time-and-keeping-it-green-while-ben-goes-amber/

"A couple bottles of champagne and two vanilla macarons later, Ben and I were curious as to whether or not we were pushing the limit of sobriety. Would they continue serving us? Hmm. From our prior flight, we learned that Emirates has a green, amber (we US Americans call it yellow), and red light system for gauging whether to serve a drunkard passenger. Ben asked one of the business class crew (whose name we were too drunk to unfortunately forgot to get) whether he was still green, and the crew member smiled a bit, laughed, and said that he was “probably amber” but that he would not stop serving him. Ben then asked another crew member, who agreed that he was amber. Poor Ben — what a light weight! Now we know why Ben’s nickname is lucky — he’s lucky he’s never been restrained on a flight for being so bad at holding his liquor. And I’m not even throwing shade. To prove my point, I’ll explain what the crew thought of me. He then asked about me. Surely I was amber too; right? Apparently I didn’t look it. Both crew members said that I was green!"

So for a crew member to cut you off, you must have definitely had too much to drink. I've never seen or heard of anyone I know getting cut off, even my heavy drinking friends.

The crew always has the authority though, I remember an SFO777 TR where he was flying DXB-JFK in F and a pax was very disruptive after having too much to drink. He was met by NYPD or security upon arrival! The crew probably should have cut him off.