Why does the YouTube app know what I have watched on youtube.com in Safari The YouTube app seems to have access to Safari's cookies because if you watch a youtube video in Safari, the app knows it. 

Is there a permissions setting to prevent this? 

Is this not an alarming permissions leak?
Your YouTube history is affiliated with your Google account. This is the same affiliation that allows you to keep track of your liked videos and any playlists you may make and channels you subscribe to. Any browsers/apps which are logged into your Google account will have the same information about your view history.