In the rust world "unsafe" is synonymous with "isn't proven to be safe by the compiler". Under this definition, every C/C++ program that uses pointers is "unsafe" because the languages make no memory safety guarantees.
unique_ptr is unfortunately still unsafe (in the Rust sense): there's nothing in the language stopping use-after-move of the unique_ptr value itself (which is a null-dereference and undefined behaviour), nor references to the interior becoming dangling.
Owned data in Rust (which is all data by default, unlike C++ which must opt-in via unique_ptr) has stronger guarantees than those provided by unique_ptr. It's still possible to deref a unique_ptr after using std::move.
That may be technically true but in practice and rhetoric "unsafe" is often used in contexts with much broader, implicit connotations. For example, putting Rust-compiler-proven-safety as the top, first, or best feature to consider. In that context, saying "C++ isn't Rust-safe" is essentially defining Rust to be "better", not advancing a coherent argument that it is in fact better.