Is directaddress.net Safe?

I am receiving email at an inactive email address I monitor telling me there are messages from other users with email addresses on the same domain, a medical practice website. Of course, you have to register to retrieve those messages. Since there is no direct link to the messages, there is no possible way any messages could be waiting for me prior to my registering. This can be nothing but a fake come-on to get me to view their "secure" email service. And the final bit of evidence? It is claiming that I sent an email to that inactive address myself. Which I most certainly didn't. This site claims to be a secure environment for communication with patients. I would no way, under any circumstances, trust anyone else's personal information on a site that markets itself this way. In fact, I wouldn't share their dog's name, let alone their health history.