You're correct that this is the stated justification most of the time. Should be nuanced though, because the working C program has a risk, but the the risk is

You're correct that this is the stated justification most of the time. Should be nuanced though, because the working C program has a risk, but the the risk is a function of the size of the codebase, its age, and the number of audits it has undergone. It is definitely easier to write bugs in C due to the additional freedom you have, but it is not necessarily a "high" risk for mature C libraries. It is definitely not as advisable to just replace all C with Rust, but it is advisable to prefer memory safety in new projects.