Each week, I livestream a video from a noncommercial Facebook business page I manage; then, I download it through Facebook's native download button (given to business pages but not personal accounts, apparently) and upload the video to YouTube. However, whenever I download my videos this way, their resolution gets lowered to 480p, compromising the picture for when I upload it to YouTube. If I could use third-party software, I could download the videos in their full resolution.
In a related thread, someone stated, "Downloading Facebook videos are not allowed by Facebook TOS. Facebook may cancel user account if it detects account owner downloaded a Facebook video."¹ (That thread is about making EULAs, while this thread is about downloading videos I own.) However, I tried to find such a statement in Facebook's terms myself but did not find such a statement.
Do I have the right to use third-party software to download Facebook videos I livestreamed? Is videoconverterfactory.com correct in saying that fair use makes their software legal for downloading videos from YouTube, Facebook, etc., even to the point of overriding the terms of service, so long as it's for personal use?²