Hey the last thing I want to do is to get into a meaningless semantics discussion however i have quite a bit of experience around this issue.
according to Microsoft direct push is supposed to "require" a GPRS or 3G connection to work. I had complained about not getting direct push using a WiFi connection and I was told that the application did NOT support this!

Apparently there are ways to get it to work if you start a WiFi connection with a phone conection and you may be getting it to work otherwise but for many with battery management going on with thier wireless connection it may not work as it didn't for me.

This blog offers more info from someone who knows way more than I do. The only reason this has been so dear to me is that I have my own Exchange server and my own GoodLink server.

Henrik Walther Blog » Blog Archive » DirectPush and WIFI connections