I had a similar experience near Tahtakale, Istanbul. They work in teams and one of them usually draw your attention away so that you are not focused on the guy behind.
I just got out of the Spice Bazaar and it was incredibly crowded. I could not even walk straight without touching anyone. Then I saw these guys almost having fight, arguing really loud. While, I was looking at them and trying to walk, I felt somebody pulled my cell phone from my back pocket. When I turned back, there were like hundreds of people behind, pushing me forward. I yelled but no help. I realized later on that the fighting scene was a scam since it almost ended immediately when my phone disappeared.