Sure, but it prevents memory safety issues, which C doesn't. As for logic bugs, what does prevent them? That's a bigger question but I'd suggest it's:

1. The ability to model your problem in a way that can be "checked". This is usually done via type systems, and Rust has an arguably good type system for this.

2. Tests that allow you to model your problem in terms of assertions. Rust has decent testing tooling but it's not amazing, and I think this is actually a strike against Rust to a degree. That said, proptest, fuzzing, debug assertions, etc, are all present and available for Rust developers.

There are other options like using external modeling tools like TLA+ but those are decoupled from your language, all you can ever do is prove that your algorithm as specified is correct, not the code you wrote - type systems are a better tool to some degree in that way.

I think that if you were to ask an LLM to write very correct code then give two languages, one with a powerful, express type system and testing utilities, and one without those, then the LLM would be far more likely to produce buggy code in the system without those features.