That depends a lot on how you define "correct C".
It is harder to write rust code than C code that the compiler will accept. It is IMHO easier to write rust code than to write correct C code, in the sense it only uses well defined constructs defined in the C standard.
The difference is that the rust compiler is much stricter, so you need to know a lot about details in the memory model, etc. to get your code past the compiler. In C you need the same knowledge to debug the program later.
My impression is that they are very aware of the state of C++ and the efforts to provide strong safety guarantees. That's why they keep raising the pressure.