When people upload videos to Youtube, they give Youtube the right to distribute the videos through third parties. The copyright issue is a primary selling point of Youtube.
The Youtube terms of service make it easy for people to share videos on social media and their person web sites. When I blog on my other sites, I routinely use youtube videos.
BTW, if you want to, you can add reviews for Youtube and Vimeo channels.
I personally do not like Youtube's dominance. I think it is better to review some of the many independent podcasts. Podcasts hosting companies generally allow for the sharing of content. You have to read the ToS.