greetings
Ill give you an example where you can use ''even though'' ... ''but''
EX - ''Even though Ive asked you many times to not put milk in my coffee, you continue to do it. Its like you arent even listening to me. But, its ok, because you make me laugh.''
Like you stated, it has to be in a different sentence. my point is there are many scenarios where youd hear an '''even though / but''. I suppose the person in the video was just talking faster than thinking.