I'm not sure if I understand. What you said makes no sense.
If it was "saved to console" (as in purchase details, since the data is definitely on the console itself --- not streamed), rather than "saved on the server" it would be the opposite of how an account system works. There would be no way to verify purchase data except through the original console.
That said, even without an actual account system the Wii still kept records of purchase data server side --- and in some cases, people were able to get games transferred from a dead/stolen console by verifying details from an associated Club Nintendo account. The Wii U, on the other hand, does have an account system (with custom user names / password) but lacks a way to log in from other consoles. (You can link a 3DS, but without assistance from Nintendo, it's currently not possible to use the same NNID on more than 1 of the same console)