This is just incorrect. The beauty of Rust is even bad programmers end up writing memory safe code because the compiler enforces it. The ONLY rule an organization needs to enforce on their crappy programmers is not allowing use of unsafe. And there are already available tools for enforcing this in CI, including scanning dependencies.
I think what they're saying is that by making devs use a less familiar language, you're going to end up with at least as many security bugs, just ones not related to memory safety. (Not weighing in either way, just clarifying.)
Keeping mind that, if you have an RCE bug, any other class of bug is irrelevant. It's a bit like diagnosing someone with the flu after their head has been cut off. And while acknowledging that you're not personally weighing in either way, I will personally call the idea that you'll end up with just as many bugs of a weaker class to be quite silly. Everyone starts as unfamiliar in every language, but not every language makes it equally easy to accidentally introduce vulnerabilities. Defaults matter, tooling matters, and community norms matter, and all of these make it less likely for a low-quality Rust programmer to introduce vulnerabilities than even a medium-quality C programmer.