Right, thanks for the helpful videos and details from the manual, I get the sense that the canon mobile app has not yet worked the video out (aka crippled), although it doesn't make a lot of sense why given that it's very much in control of all the camera's functions, and EOS Utility allows you to shoot video, no problem (no digital zoom possible on the T3i).
Given that there are non-Canon apps that also allow control over the camera, including video like http://dslrcontroller.com/
with a wired connection, my guess is that someone, and maybe eventually Canon, will come up with a great iPad app that will allow remote video shooting.
In the mean time, I wonder if it would work to turn on Live View so you can monitor the focus and exposure on your iPhone or iPad, then when you want to trigger the video, you do so manually on the camera. Although, this wouldn't allow truly remote video shooting, it would likely work just fine for most applications where you just want to use the iPad as an off camera monitor and controller. This does not work on EOS Utility as far as I can tell, but maybe there's a way to allow control from both the computer and the camera.