I've been in situations where I was sure this was true. I've also been in situations where the person claiming it simply refused to become competent in the language, framework, or persistence technology that the system was built on.
Also subjective: "The business needs a capability the current code was never shaped to grow into." Most of the times I've heard this brought up, it's not that you need a re-write, but you need a re-architecture. Often the existing system can continue to do its job as it always has, but in a new architectural context. Or 90% of the code can stay the same, while the application it runs in is changed, for example from a web service to a Kakfa consumer. (This is why it's so important to avoid languages and frameworks that are tightly bound to an architectural choice.)