By now, we have learnt the hard way that this might indeed be a fallacy of composition. Let me give you just one example. Imagine that a certain asset suddenly becomes more risky. Each bank that holds this asset might react prudently by selling it. However, if many banks react that way, they will drive down the price of the asset.
This will amplify the initial shock, might affect other assets, and a full-blown crisis might result. Each bank has behaved prudently, but their collective behaviour has led to a crisis. The business of banking is ripe with externalities, with potential herding and with contagion.