I can build black box ciphers with the following properties:
Satisfies SAC, but is trivially weak (a keystream from an LFSR seeded with the key).
Does not satisfy SAC, but built from secure primitives (Base64 encode the output of AES).
From 1 you can see that SAC is not sufficient for security. From 2 you can see that SAC is not necessary for security.
Since neither $SAC \implies Security$ and $Security \implies SAC$, what conclusions can you make based on SAC?