First, I was talking about useful definitions of thread safety. That was language-agnostic, not related to Rust. And if absence of data races were all that Rust guaranteed, then Rust indeed wouldn't be much of a help. What Rust actually does is require you to be (fairly) explicit about threads interacting with each other, which is a much stronger type of guarantee [1]. Rust comes with a default setting derived from the general shared-xor-mutable principle that threads don't mess with each other's data without permission, which makes it easier to reason about thread interaction.
Second, the OP was comparing Rust to actor languages. Actor languages also don't have data races and don't require mutexes (because the memory spaces of actors are disjoint and actors themselves are sequential). In fact, actor languages provide even stronger guarantees, as actors can only interact with each other at well-defined points. "Fearless concurrency" hails back to the 1970s. It is not a new invention, nor is it unique to Rust. It is great that Rust supports it, but I really wish people would stop talking about it being novel and unique.
[1] Which is not to say that Rust's choices don't come with tradeoffs, but then, in the area of concurrency, you cannot realistically avoid tradeoffs. In Rust's case, as with actors, the primary tradeoff is performance for safety.