> The correctness statement is not helpful

But... that's everything, and why it's included.

Undefined behavior from asynchronous computing is not worth study or investment, except to avoid it.

Virtually all of the effort for the last few decades (from super-scalar processors through map/reduce algorithms and Nvidia fabrics) involves enabling non-SSE operations that are correct.

So yes, as an abstract term outside the context of computing today, asynchrony does not guarantee correctness - that's the difficulty. But the only asynchronous computing we care about offers correctness guarantees of some sort (often a new type, e.g., "eventually consistent").