Integer overflow cannot result in memory safety violations in Rust.
And even wrt memory, Rust (with the standard library) is not free of its own warts, see the OOM situation. See e.g https://news.ycombinator.com/item?id=10545877 for a discussion on this.
Just to be clear: I generally like the ideas of Rust. I just dislike its presentation by some as a magic solution to all kinds of concerns.