No. Rust's ownership problem solves it for trivial cases, at the cost of making it hard to do other things (such as sharing references past the lifetime of the owner without resorting to Rc<T> or Arc<T>, at which point you don't really have lifetime guarantees anymore).
The essential limitation of Rust is that (without resorting to Rc<T> and Arc<T>, which would put you back to square one) it is conceptually limited to the equivalent of reference counting with a maximum reference count of 1. In order to make this work, Rust needs move semantics and the ability to prove that an alias has a lifetime that is a subset of the lifetime of the original object) and may even sometimes have to copy objects, because it can never actually increase the (purely fictitious) reference count after object creation.
This inherent limitation makes a lot of things hard (or at least hard to do without copying or explicit reference counting). Structural sharing in general, hash consing, persistent data structures, global and shared caches, cyclic data structures, and so forth.
In short, you have the problem with shared references less, because Rust makes it hard to share data in the first place, for better or worse. (Again, unless you resort to reference counting, and then you get the issue back in full force.)
