In a way both of these viewpoints are correct. In another way they are both wrong. To see how, let's split this issue into two parts.
A human being can write faster code than a compiler for any given program
This one is fairly easy to prove (semi)formally. Suppose you have a program P written in some programming language L that runs faster than any hand written version. A human being can look at the assembly output of that program and write an equivalent source version in straight C. Usually when doing this you find some specific optimization that you can add to make the hand written version faster.
Even if the compiler's output were proved optimal (such as in the case of superoptimization), it can still be matched by copying the output into your own program as inline assembly. Thus we have proven that for any program humans will always be faster.
A human being can not write faster code than a compiler for every program
Let's take something like Firefox. We know from the previous chapter that one could eschew complex compiler optimizations and rewrite it in straight C or equivalent and end up with better performance. The downside is that you would die of old age before the task would be finished.
Human beings have a limited shelf life. There are only so many times they can press a key on the keyboard until they expire. Rewriting Firefox to code that works faster with straight C than the current version with all optimizations enabled is just too big of a task.
Even if by some magic you could do this, during the rewrite the requirements on the browser would change. A lot. The end result would be useless until you add all the new functionality that was added since then. This would lead to eternal chasing of the tail lights of the existing project.
And even if you could do that, optimizing compilers keep getting better, so you'd need to go through your entire code base regularly and add the same optimizations by hand to keep up. All of these things could be done in theory, but they completely impossible in practice.
The entire question poorly posed
Asking whether compilers and humans write faster code is kind of like asking which one is "bluer", the sea or the sky. Sure you could spend years debating the issue on Twitter without getting anywhere, but it's not particularly interesting. A more productive way is to instead ask the question "given the requirements, skills and resources I have available, should I hand-optimize this particular routine or leave it to the compiler".
If you do this you rediscover the basic engineering adage: you get the best bang for the buck by relying on the compiler by default and doing things by hand only for bottlenecks that are discovered by profiling the running application.
PS. Unoptimized C is slow, too
Some people think that when they write C it is "very close" to the underlying assembly and thus does not benefit much from compiler optimizations. This has not been true for years (possibly decades). The performance difference between no optimization and -O2 can be massive, especially for hot inner loops.
When people say that they can write code that is faster than compiler optimized version of the same algorithm in some other language, that is not what they are actually saying. Unless they are writing 100% pure ASM by hand  that is not what they are saying. Instead they are saying "I can take any algorithm implementation, write it with an alternative syntax and, when both of these are run through their respective optimizing compilers, end up with a program that runs faster".
 Which does happen sometimes, especially for SIMD code.