This is not how it worked, no. It was never memory leaks per se that led to unsoundness there. It was skipping destructors. You could have the exact same unsoundness if you freed the object without running the rest of its destructor first.
That part was the design choice Rust made- make destructors optional and change the scoped threads API, or make destructors required and keep the scoped threads API.
There is an underlying definition of memory safety (or more generally "soundness") that precedes Rust. It is of course defined in terms of a language's "abstract machine," but that doesn't mean Rust has complete freedom to declare any behavior as safe. Memory safety is a particular type of consistency within that abstract machine.
This is why the exact set of undesirable-but-safe operations varies between memory-safe languages. Data races are unsafe in Rust, but they are safe in Java, because Java's abstract machine is defined in such a way that data races cannot lead to values that don't match their types.