This is exactly the pattern of calls to the hash function inside HMAC: Hash( (K' xor opad) || Hash( (K' xor ipad) || m ) ).

This clarifies that the simulator can only simulate calls to Hash that have this form, i.e. that are done from within HMAC. It cannot consistently simulate calls of a different form, i.e. that are done directly.

The consequence for a protocol that uses this theorem for its security proof is that the hash function cannot be used directly for arbitrary calls.

This works because internally, the key will be padded up to the block length. Then, there will be at least one byte where the two different paddings can be distinguished.