Lightning network consensus mechanism for payments that run across multiple nodes

In the HTLC protocol of the Lightning network, there is a transaction in which the money is routed from A via B to C. C creates a secret and generates the hash of it with SHA-256, then C passes the hash on to A. A passes this hash on to B. Now B must reveal the secret to authorize the payment to B, and B then passes the hash to C. C must then reveal the secret in order to receive the payment. But how can the secret be presented if only C knows the initial value? Is the initial value passed on to every participant, but not to A?