Bugs would be found in a Rust codebase all the time as well. The difference is that a certain class of bugs is going to be absent from safe usage of Rust. (Unsafe Rust gives you just as much rope to hang yourself with as C).
By the way, Rust devs are working on a mathematical formalization of those rules. Here's a blog post about a part of this effort: https://www.ralfj.de/blog/2018/07/24/pointers-and-bytes.html. (There are similar formalization efforts for subsets of C, that led to software like the CompCert verified compiler)