When you are trying to sync video back to the iPhone from the computer, those videos have to be identified in the Movies section of iTunes. Then they would be accessed on the iPhone via the Videos app on the phone, not in the Photos app. With the phone connected and selected in iTunes, go to the Movies tab in iTunes, and select the video you are trying to sync to the phone. If you cannot see it there, then you need to add it to iTunes. Just importing them to the computer does not add them to iTunes. Just like importing photos does not add them to iTunes. But with photos, iTunes just acts as a funnel allowing you to select folders from the Photos tab and then syncing. Movies/videos requires you to add them to the iTunes library before you can sync.