Can an e-mail title 'turn off' a secure Internet connection?

You go to Earthlink’s WebMail and it gives you a Secure connection. Then when you log out, the exit Security Alert pop-up warns you that you are leaving it.

Now sometimes the exit Alert comes up within WebMail when it is just loading the list of received e-mails (in my case, spam at a ratio of 40 to 1).

So can a spammer put something into the Subject or From information that would turn off the security?