Rust doesn't do anything magical to the security of programs written in it. Rust simply won't allow you to compile quite a lot of vulnerable programs that would be happily compiled by a C compiler, because the language is a lot stricter in terms of memory and thread safety.
Also, "safety" of Rust actually requires you to be rather more than less competent. There's a rather steep learning curve, less competent coders will struggle (and learn a lot in the process) just by trying to come up with a code that will be finally accepted by the compiler. Rust doesn't provide safety by holding your hand and doing stuff for you - it's more like a strict parent that sets up boundaries of how you can play, so you won't hurt yourself, but otherwise leaves you alone.
Of course it doesn't mean that you can't write vulnerable code in Rust. It's just a bit harder to do it by accident for some class of potential issues.