Well, I finally broke down and started using Tenet’s Exchange Server. First, IS created an Exchange account for me then I tried adding it to my iPhone. After I got the settings right, from someone who’s using it with their iPhone everything works fine.
Here are the settings that aren’t obvious.

Server mail.etenet.com
Domain tenethealth

Then make sure SSL is on and you should be good to go with your email address, username and password.
Now, if I could just get this working on my Mac desktop. There are clearly some differences in the manner in which iOS 4 and the OS X 10.6.4, and particularly Mail.app, iCal and AddressBook, interact with the Exchange server. I’m still trying to find the secret incantation to make it work on the desktop. When I do a follow-up will be forthcoming.
BTW, the above settings should work just fine for your iPad too.
Update:
Make sure your username is not your full email address.