I have tried it but

Yeah, I’m still puzzled by that.

I just tested your theory – I created a new user on my My Cloud, did NOT set a password.
Then, on the share automatically created for that user, I set it to PRIVATE, with only that user having access.

I was able to connect to it from a Windows 7 Home Premium x64 client with no issue at all – no password needed.

Connecting to share:

Challenged for credentials, for which I provide ONLY the user name…

Connection immediately successful, and I can create and manage files in that share: