Yes, email is insecure, and should not be used to deliver sensitive data. That doesn't mean that they should need to refuse to send anything via email, but given HIPAA and the potential penalties for non-compliance, I'm not surprised that some providers would choose to err on the side of extreme caution and shun email entirely.
Here is why email is insecure: The provider does not control the entire channel. Once an email had left their system, they have no way of guaranteeing that it will be encrypted and protected from prying eyes as it wends its way through the Internet and to your inbox. In fact, with the state of email today, its quite likely that it will not be encrypted along the entire transit path. Hence, if they were to send PHI via email and it was stolen or misused, it would not be unreasonable to argue that they failed to show due care and should have known better, thus, be held liable for the leakage. When you're looking their web site in a browser, they can confidently assert that the information is being delivered securely to your screen by using HTTPS.
This risk can be (virtually) eliminated through the use of encryption such as PGP. Do you know what the uptake of PGP is? Percentage-wise of all email-users, in the low single digits at best. And even those users tend to hate it and view it as a necessary evil. That may change in the future, but that's the reality today. Do you know what the uptake is for HTTPS use over the web? 100%. Every browser supports it, and it's completely painless for the end user. Use what works for your users.
Is snail mail more insecure? No. Why not? Because the piece of mail has a single physical location, and can't be stolen without the physical presence of, and personal risk to the thief. Stealing things off the Internet is easy. That network captures trap, and mail servers log unencrypted email is not so much a risk as it is a given. Snail mail is very unlikely to be intercepted. The USPS has an entire law enforcement division to protect it. They have a stellar (not perfect by any stretch of the imagination, but very very good) record of delivering mail to the intended recipients. It is reasonable for a company to entrust the USPS to deliver confidential information to you unmolested. It is not reasonable to expect the same from SMTP email.
So, yes, the fact that they won't provide any information to you over email is excessively conservative. The fact that they won't provider PHI that way, is certainly not.