We are saying the same thing. H0 is SHA-1 in your example.

The strength of an HMAC depends on the strength of the hash function; however, since it uses two derived keys, the outer hash protects the inner hash (using the same hash function), which in turn provides protection against length extension attacks.

The case I was making, is that weakhash(stronghash(m)) has the security of weakhash, no matter how strong stronghash is.