Yes, you're right. All players do see at least one blue hat. But, the puzzle depends on this:

C is trying to determine if the other players see one blue hat or two blue hats!

Another thing that might be confusing you is that this is a proof by negation. The proof isn't that C has a blue hat on his head. The proof is that C doesn't have a white hat on his head. Since !white == blue, C has a blue hat.

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We are the carpenters and bricklayers of the Information Age.

Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.