No, the Rust community almost universally understands "safe" as referring to memory safety, as per Rust's documentation, and especially the unsafe book, aka Rustonomicon [1]. In that regard, Safe Rust is safe, Unsafe Rust is unsafe, and C++ is also unsafe. I don't think anyone is saying "C++ is all unsafe."
You might be talking about "correct", and that's true, Rust generally favors correctness more than most other languages (e.g. Rust being obstinate about turning a byte array into a file path, because not all file paths are made of byte arrays, or e.g. the myriad string types to denote their semantics).
[1] https://doc.rust-lang.org/nomicon/meet-safe-and-unsafe.html