For example, why does Coinbase require 6 confirmations for a Bitcoin transaction to be awarded instead of just 1? Is 1 confirmation not proof that the transaction is legitimate?

Or is there something more to this that I am missing?

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    A single confirmation is proof that the transaction is valid (because it was included in a block). But, with only one confirmation the risk of a double spend happening is very high. Here you can read more about double spends and how they work: Link – thesys Apr 7 at 17:38