Apple ID 3rd Gen - sync new purchases

I have the new 3rd generation Apple TV. The movies that I owned before I bought it now show up under Moves > Purchased, but any movies I bought since then aren't showing up. I can stream them from my computer if I keep my computer on, but I can't figure out how to sync them. The only help articles I've found are for first and second gen and the software isn't the same (it says to select "Sources > Syncing" on the main menu and mine doesn't have that).

It also doesn't show up as a "Device" in my iTunes menu, but if I play a movie from iTunes, it plays on the Apple TV (but, again, I'd have to keep my computer on to do that).

This article would be awesome, except it's only for first gen: http://support.apple.com/kb/TA38571

This article is for 3rd gen but doesn't tell me what to do if the movies AREN'T under purchased: http://support.apple.com/kb/HT5183

I have the latest version of software on both the Apple TV and iTunes on my Macbook Pro. I also rebooted my Apple TV and that didn't help.

Suggestions??