I believe that the tech's you're talking to aren't quite giving the correct information. Direct Push simply establishes and maintains a persistent HTTP/HTTPS connection between your device and the server. As I'm writing this, I'm staring at the Comm Manager on my TyTN II with the phone and data connection shut down, WiFi active, and the "Direct Push" lit up indicating that the connection has been established. I've also just shipped myself a test message to my Exchange account.

Where this may be coming from is the reason that Direct Push was developed by MS. Previous push mail with Exchange required the use of SMS messages to trigger the mobile device to initiated a synchronization. This chewed up messages, which required either per-message charges or increased costs for messaging plans. So Direct Push was developed to leverage the cellular networks and eliminate this need. But since it's based on IP and HTTP, there's nothing tying it to a cellular modem or connection. Where WiFi may fail you is that it's put to sleep by the standby mode, while the cell lines aren't. So when it wakes up, the first thing it does is reestablish the connection and the mail flows.

My $.02 anyway - find a WM device that doesn't put WiFi to sleep, and Direct Push will work the same on that as it does on a cell network.