This is false.
Neither C# nor Rust protect from memory leaks. There are actually some gotchas in C# that can cause memory leaks - for example, you have to be very careful about events. Memory leaks are not memory unsafe, though.
On the topic of actual memory safety - C# has unsafe blocks just like Rust does. Safe Rust is just as safe from memory safety problems as safe C#, even more so, because C# doesn't require unsafe for FFI, where all bets are off. And unsafe C# is just as unsafe as unsafe Rust can be.