It didn't work.

My iPhone was talking to the television, and even informing me it was casting, and all that stuff, but the television continued playing something else.

Rinse and repeated many times with the same results until I noticed a small prompt on the television asking for permission to receive the signal. I was so focused on the iPhone, I totally missed it. I pressed the accept prompt, or something, and viola, it worked.

Just an idea.

If your iPhone isn't using WiFi (e.g. cellular data only), then it probably won't find the Tv.
If both the TV and the iPhone are on the same WiFi, it "should" see it.

I'm assuming you're talking about sending the video to it vs. actually trying to sync files

Disclaimer: I'm using an Apple TV (the set top box, not the service) and a Mac. Your milage may differ.