You are, of course, right. And this distinction is important for this chain of comments.

Though, in fairness, that is /kind of/ like transmitting it---in the sense that it impacts the message that is returned. It's more akin to sending a checksum of the magic number, rather than the magic number itself. But conceptually, that is just an optimization. The desire is for the client to ensure the server is using the same magic number, we just so happen to be able to overload the signature to encode this data without increasing the message size.