Why is SIV a thing if MAC-and-encrypt is not the most secure way to go? The question that I am asking is exactly what I ask in the title.
Skimming these three papers should give you an idea (which I list roughly in the order I recommend you look at them):


Rogaway, Philip.  2004.  "Nonce-based symmetric encryption."
Namprempre, Chanathip, Phillip Rogaway and Thomas Shrimpton.  2014.  "Reconsidering Generic Composition."
Bellare, Mihir and Chanathip Namprempre.  2000.  "Authenticated Encryption: Relations among notions and analysis of the generic composition paradigm"


To make a long story short, results about generic composition of encryption and authentication are very sensitive to how you define the concept of "encryption."  In a classic textbook definition, encryption schemes are defined in terms of probabilistic algorithms.  As the Rogaway paper puts it:


  Ever since Goldwasser and Micali’s landmark paper [7], formalizations of encryption schemes have usually made the encryption algorithm probabilistic or
  stateful. In this paper we investigate a different formalization for symmetric encryption: the encryption algorithm is made to be a deterministic function, but
  one of its argument is a user-supplied initialization vector (IV). Effectively, the user and not the encryption algorithm is made responsible for flipping coins or maintaining state.


The Bellare and Namprempre's famous result that encrypt-then-MAC is the only secure composition uses the classic, probabilistic framework for encryption.  But if you start from Rogaway's IV- or nonce-based definitions, as the 2014 Namprempre et al paper does, you get more nuanced results.  Some but not all versions of MAC-and-encrypt—including SIV—turn out to be secure, whereas all versions of encrypt-then-MAC are secure.  As the paper puts it:


  One might interpret our results as saying that the conventional wisdom—that Encrypt-then-MAC is the only safe GC method—is wrong, an artifact of early work having admitted sloppy schemes and considered only pE+MAC → pAE conversion. An alternative interpretation is that the conventional wisdom is essentially right, that Encrypt-then-MAC is the only safe GC method, for it works across multiple definitional settings, whereas the story becomes nuanced for other GC schemes.
  
  Nothing in this paper should be understood as suggesting that there is anything wrong with BN. If that paper has been misconstrued, it was not for a lack of clarity. Our definitions and results are complementary.