Total bullshit (and I guess that's your point, because it wasn't labeled as such). The first thing the guy's companions would have done would be to grab him and shake him awake. Instead they just stand around while Brown emerges from the back room, exactly as though they'd been asked to. And then Brown starts issuing orders for what amounts to a kidnapping? Maybe it gets more believable after the four-minute mark, but that's where I tuned out.
The wallet-steal trick I believe, because it only involved one mark. All Brown had to do was film dozens of attempts until it worked. Nothing new there -- Zimbardo and Milgram showed that if somebody refuses an order to do something silly, dangerous, or immoral, all you have to do is ask somebody else. It won't be long before you find a willing stooge. On the other hand, it might take months before you find an entire group of still-sober people (who just walked into a pub) who will play along perfectly with a complicated trick.
I actually agree with you that Zimbardo and Milgram are relevant to the wallet-steal trick. Keep in mind that the studies you are referencing didn't involve random strangers being told what to do, they were people who had applied to take part in a study, were pre-screened and were being paid for their time. This is also how I suspect Brown's scenario played out, this man almost certainly went through a similar process and knew he was being filmed but was not acting according to a script.