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I can build black box ciphers with the following properties:

  1. Satisfies SAC, but is trivially weak (a keystream from an LFSR seeded with the key).

  2. 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?

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    $\begingroup$ What about: the SAC is useful only in limited context, like internals of a cryptographic primitive? $\endgroup$ – fgrieu Sep 28 '16 at 17:11
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As pointed out in the comment, SAC is just one criterion relevant to diffusion, useful in ciphers as well as hash functions but by no means enough to provide security under any reasonable definition.

Just a partial list of desiderata for Sbox function design, optimal nonlinearity, high degree, low differential probabilities, high degree as a univariate polynomial, algebraic immunity, correlation immunity, etc should be enough to convince one of this.

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