I have no idea, and probably won't be able to help with this one, but I do have a few questions that might help you, or someone else, answer the question.
Since you can't see the video quality in the Photos app, you are obviously opening them somewhere else, or doing something else that allows you to see the video quality. If you'll share what you are doing, and how you are seeing the video quality, perhaps the problem can be narrowed down a bit. Even if it only proves that the iPad really is taking 720p when it should be 1080p.
The only advice I can give you, if the Camera app is for certain the culprit, is to try Settings > General > Reset > Reset All Settings. This should force any settings glitches back to default, and since 1080p is the default this might do the job. Reset All Settings won't delete anything or change your account settings, but it will default many other settings. You'll probably have to tweak things back to the way you like them afterwards.