Why are Saturn's rings in one plane?

Why are Saturn's rings flat? I was reading / gawping at the utterly stunning Cosmos over the weekend, and found the inklings of an answer. This site seems to confirm it: because particles and objects in many random orbits will eventually zoink each other out of their opposed planes, becoming more inclined, until eventually everything settles into one stable arrangement. Does it count as being an emergent phenomenon then?

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