Cobol is a programming language, not an operating system like macOS. It's no more solid than newer ones like C (yes, C is "new" compared to this) or Java but actually a lot more fragile in practice. More importantly, it keeps away new people and entrenches SWEs who are familiar with the codebase. Actually the real problem isn't the language itself, but it's a good indicator of their bad environment.
Doubtless that their code has all kinds of security vulnerabilities guarded by secrecy alone, just waiting to surface. And yes, I've seen many issues with banking sites, but that's probably not the Cobol talking.