Yes: in fact, any memory-safe language can guarantee that a “safe” program would not have this class of bug. In languages without pointer arithmetic and with bounds checking, this type of bug just isn’t possible. Not only does this include Rust but also Java, Go, and a fairly large list of other programming languages.

Most of what Rust improves on is related to memory ownership and concurrency - we’ve had ways to prevent this class of problem for a long time, and in fact there are even C variants that can do that too.