Isn't that a bit like saying that it "can outperform equivalent assembly"?
No; as shown in the link, this work allows idiomatic Haskell to outperform idiomatic C. Obviously it's possible to write C which is a direct translation of the generated assembly, but such code would be nearly unmaintainable, and certainly very difficult to reason about.
And why can you not prove the equivalent C correct?
Proving the correctness of C code is possible, but (in my experience) significantly more difficult than for Haskell.
After all, you're doing that proof by hand either way. A Haskell compiler will only help you prove that your program is well-typed. If you're mutating buffers then you're in a monad like IO or ST and the the compiler will throw it's hands up and tell you that correctness is entirely your problem.
I don't mean that the compiler will automatically generate a proof for me, but that authoring a proof will be possible in practice -- as opposed to C, where it's possible in theory but nobody actually can.
I'm a bit confused about why you think operating within a monad causes problems for proving correctness; to my knowledge, verifying code which uses monads is no more difficult than code using any other data types.