Under normal conditions, when people walking in front of you stop, you stop also so you don't bump into them. Makes sense, right?
So you would think that as long as everybody obeys that simple rule of movement, this should never happen.
But having been caught in a much less serious "crush" once, I know it's not that simple.
In my case, I was at a similar event -- religious in nature, lots of people from all around the world, and mostly traveling in groups -- and although everybody was polite and non-aggressive, as groups traveled through the crowds, nobody wanted to be separated from their groups, and that caused major issues.
For instance, a lot of groups traveled while holding hands in an effort to remain together. But imagine how much more difficult it is for a bunch of worm-like people chains to travel through a crowd than it is for discrete individuals to do so.
The surge I was caught in was little more than a momentary push forward, but it was very scary to lose control over my ability to move freely.
I would hope that with most people having cell phones nowadays, which gives them the ability to more easily regroup after separation, it should be a priority in cases like this to urge people to not form chains and to devalue staying with their group if it affects the flow of traffic.