HI,
The router needs to know where to send the email too, hence your email.
Also, it needs to connect to an email (SMTP) *server (such as google) to send the email. ISP's and Web Based Email providers require users to log into their account before sending email to reduce spam through their network. I have never had a problem entering these details in all the various routers I have owned over the years.
If you are that concerned, just open a web based email purely for this feature, however from my view a little unnecessary.