Here is the problem, "in an e-mail from Jagex". When they repeatedly say that they, Jagex, will never e-mail you, they mean it. No matter how legit it looks.
Besides if you are tieing an e-mail to your account to confirm, or if you are recovering your account using your e-mail I guess, idk how it works. Then you'd get real e-mails from them.
Jagex doesn't ever send emails. Don't believe anything you read in an email that looks official, because it isn't. Also, don't click links in those emails, because they can steal your RS account.