Do you know any big code base without bugs? That's not exclusive of C, e.g. check any big Java code base. Regarding Rust, I would like to see the kind od bugs that would arise in big code bases (thread contention, performance issues, etc.).

I have to say that I feel as if the problem here isn't competent programmers though. It's competent testing that is lacking.

Sure, it's possible to make a lot of stupid mistakes in C, but most of these mistakes should be found in testing, before the code is deployed. You'll probably say that "We don't even have those problems in language X." and I agree, but you should run the same tests no matter the language, because you want to find as many problems as possible, even if you write your code in language X.