It requires a bit of extra work, but I found a way to do it. I guess the key to doing this is to have the video in the correct format.
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-1) First, be sure the video is in a format that is designed for iOS devices. (This is where most of the work is found to be) In my case, I used a video I made myself in Vegas Movie Studio. I took the old video which I rendered originally for YouTube and re-rendered it in a pre-set format and codec for what's labelled as "iPad/iPhone 4 720p". I imagine virtually any editor can output to a format like this as long as you are given an option to change.
(What follows has probably been said before, but I'm saying it here just in case)
-2) Next, attach the file in an email to yourself. In my case, there was a 25MB limit, so if your file ends up being too big, try lowering the resolution or trimming down the length somehow. I have found that manually adding the file to the device via plugging it into a computer does not work in ANY case.
-3) Open the email on your iOS device, and it should automatically start to download.
-4) When it's finished downloading, open the video in the email, and click the icon in the bottom left that looks like a square with an arrow protruding from the top (I don't know what its official name is). This should give an option to save the video. Tapping that will place the video in your camera roll.
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If this doesn't work for you, I don't know what will. :\