This is why I get a little uncomfortable when people suggest Rust fixes tons of security issues. Yes, it will fix some of them. No, just because a Rust program compiles doesn't mean that it won't have problems. Rust is _memory safe_. Nothing more, nothing less.
I feel like you're undervaluing memory safety. Memory safety prevents most (all?) exploits that lead to remote code execution. There can still be high level vulnerabilities, but guaranteed memory safety is a huge improvement. Rust's type system can be used to prevent high level attacks too. For instance, if an sql library is set up properly, it can prevent sql injection by requiring inputs be properly sanitized.
I'm just very careful to not suggest that memory safety is the end-all, be-all of errors. The Rust compiler will help you out, but it's certainly not perfect.