The kind of mistakes that good programmers make are not normally caught in code reviews. That's pretty much the definition of a good programmer; their mistakes are rare and subtle.
I think the opposite is true. Good programmers know where the risks of subtle bugs are, and will use the appropriate tools (e.g. good use of a decent type system, well documented code with well designed abstractions) to make completely sure they don't exist.
This just leaves simple stupid bugs in the parts of the code where any such bug will manifest itself quickly and obviously, exactly the kind of thing caught by code review.
Another way to put it would be: good programmers design their code in such a way that all bugs are catchable by code review.
That's just arrogance. Good programmers make stupid mistakes all the time as well. It's the ability to recognize and fix such mistakes that separate "good" programmers from "normal" programmers and that's precisely where code review comes in.