I tend to see Menezes and Koblitz as having three different arguments against the common focus on provable security. In roughly increasing order of importance.

1) "Provable security" is a misleading term. Those well versed in the field understand that it is a computational proof of a mathematical object, not in anyway a statement of the practical security of an algorithm when implemented in computer code. However, many people misunderstand this to mean "unbreakable" or "perfect". Menezes and Koblitz see it as too frequently acting as a marketing gimmick, something that allows vendors trying to sell security software to say "it's based on provably secure algorithms" without anyone understanding what that means. To them, the misleading quality of the term outweighs its value. I generally disagree with them on this point, not because the point isn't well taken, but because it is far too common for phrases from academic discourse to be misunderstood outside the specific field (e.g., teleportation in quantum mechanics) for such a semantic argument to carry any weight with the specific case of provable security.

(2) Provable security proofs have frequent gaps/the authors do not recognize important assumptions they are operating under. Their "Another look..." papers focus on these cases, and it is somewhat widespread. Most of the concerns tend to be completely academic, and don't open any practical attack vectors, however their point tends to be that computational proofs are dependent on assumptions that allow a positive proof of a negative, and if the methods of the proofs sufficiently obfuscate those assumptions to where their practitioners frequently miss them, it calls the validity of the arguments into suspect. The best example of this is probably their discussion in the original 'Another look at "provable security"' article linked to on the right of the proof of Optimal Asymmetric Encryption Padding (OAEP, required since textbook RSA and other asymmetric encryption algorithms leak information about the plaintext, in RSA's case, the Jacobi symbol). It's hard to argue with their evidence, and their work has definitely led to a much more critical eye of the proof justifications and assumption discussions given in newer articles.

(3) "Provable security" misses the point. To Menezes and Koblitz, the goals of cryptography mean it shouldn't be treated as a discipline of mathematics, and while academic cryptographers chase the abstract goal of provable security and debate the philosophical strengths of computational vs. information theoretic arguments, "real-world" cryptographers, including those working for the intelligence establishments, focus on useful goals like efficiency and ease of implementation in software and hardware. To them, building cryptosystems using primitives with strong heuristic arguments for their security which are easy to implement is far more beneficial for security than the most perfectly crafted mathematical algorithm will be. In addition, although the academic field of cryptography can easily adapt to any new result which challenges basic assumptions (say, a result attacking the hardness of the DLP or factoring), all the systems relying on those assumptions in practice will be broken or greatly damaged, so holding those assumptions as central to total security is problematic. As someone particularly interested in how cryptographic systems delegate and understand trust, this argument carries a lot of weight with me, and is part of the reason that although I consider having a solid understanding of the theory and practice of provable security to be a necessary piece to greater understanding of the field, my short and longer term interests in cryptography are focusing around secondary qualities cryptosystems and their primitives.