Why do you not get the option to watch video you have taken on the phone on apple tv like you get with any other video you have put on the phone
The videos stored on your phone are already compressed, videos taken are still in HD so it wont let you view it because it would take nearly forever to send to your tv at 1.98/ mbs (average wifi speed).
IOS 4.3 (currently in beta) has settings that will allow you to do this by first routing it through your computer to be compressed but it is still sluggish.
you can fix it for now by syncing your phone with iTunes, than all your video will be viewable over apple tv
Question: If I take a video with my iPhone and simply sync it on iTunes, those videos will automatically be accesible on the my ATV? Theres nothing more I need to do other than sync it?
In my experience, no. On windows at least, iTunes doesn't automatically copy pictures or video off of the iPhone. You will have to manually open up the iPhone in explorer, and copy your pics and vids to your computer, and/or iTunes.
You have to sync with iTunes !