That's not true. In Rust you can have globals, but you have to declare the synchronization semantics for every global when you do. (That is, they have to be read only, or thread local, or atomic, or protected by a lock.)
This property makes it very easy to take a single-threaded Rust program and make it multithreaded later, and in fact this is how most Rust programs end up being parallelized in my experience.