Incorrect, the historical origin of the @ symbol was a symbol this "at the rate of" use.
The proper pronunciation is the one that matches the use you're using it in. So reading off an invoice from "Back in the day", you might say "at the rate of". Saying it in a user name or email address the proper way to read it is "At", as that's what people will understand.
I prefer the pronounceability of @ over ~