Not incorrect at all.
To use such videos, you need to actually contact the uploader and get them to give you a copy from their hard disk. YouTube doesn't give a facility for anyone to download videos they don't own unless itmobile app; and that is for offline viewing only.
The portion of my post in parentheses was a direct paste from the YouTube Terms of Service @offbeatbryce; so are you saying that YouTube itself is lying? And you actually can be terminated for using a third party app to download videos from YouTube.
Since you don't want to believe me, I invite you to go to the current incarnation of the YouTube Support Forum, found at:
Official YouTube Help Center where you can find tips and tutorials on using YouTube and other answers to frequently asked questions.
support.google.com
and ask the same question there.