Forward secrecy in Merkle trees vs. hash chains

Say we have a one-time password authentication system that uses a Merkle tree. Assume that the secret keys are of the form {sk0, sk1, ..., sk7}, and at time t = 3 an attacker recovers sk6. Will he/she be able to recover any of the previous secret keys (ie sk3, sk4, sk5, and sk6)?

My guess would be no, since all Merkle tree would do is provide confirmation whether the root value computed from sk7 is equal to the one stored on the server. Would the adversary somehow be able to recover any other key?

Follow-up question. What if a simple hash chain is used? I assume the answer to this would be yes as to get to k0, we would have to be able to calculate all the previous hashes (which includes sk3, sk4, sk5, sk6).