--from my knowledge of HIPAA, that e-mail is off limits.
Password protected e-mail systems on both ends certainly qualify as "private"; at least as private as phone conversations, given current eavesdropping technology. They're certainly more private than faxes, and I have certainly had doctors who will fax lab resutls to a patient with the patient's consent. (I have also set up a fax to e-mail number through E-fax for that reason.) And, there are doctors who communicate by e-mail. Among those that don't, I think they are just uncomfortable with the technology--or, more likely, especially in your case, they're just trying to get you to come in for another office visit so they can bill you, and insurance, for it. THAT'S my suspicion when some secretary says the doctor "doesn't practice over the phone".
There are a lot of things about HIPAA that doctors and their staff tend to believe that are patently false. For instance, I've been told by some medical office staff that the doctor cannot send me or give me a lab result without discussing it with me first, and that this is a HIPAA regulation. It absolutely isn't--and I tell them it's simply their office regulation, and to read their HIPAA material better (and I always politely offer to send them some).
I like to start them with this article:
http://www.nytimes.com/2007/07/03/he...5NKiKQSE3tX6cg
I will even send them the entire original act:
http://aspe.hhs.gov/admnsimp/pl104191.htm
The point is, HIPAA, in sum, is designed to prevent discussions or revelations of individual medical info WITHOUT THE PATIENT'S CONSENT. If the patient consents, this flow of info is not to be diverted. It's why I often given a new doctor a letter stating that s/he is allowed to discuss my medical condition with other docs I have, members of my family, and even a few friends whose judgment I trust in the event I'm incapacitated.
The other stuff that is claimed in the name of the statute is bogus (as the article describes), and has already led to some troublesome lawsuits--exactly the opposite of the original intention.
I suspect your doctor's office is just being hidebound (and greedy).