The main threat to your privacy induced by BitTorrent lies in your IP address being stored in the instance's BitTorrent tracker as long as you download or watch the video.
The recently added video <x id="START_LINK"/><x id="INTERPOLATION"/><x id="CLOSE_LINK"/> has been <x id="START_LINK_1"/>automatically blocked<x id="CLOSE_LINK"/>
the sharing system used for this video implies that some technical information about your system (such as a public IP address) can be sent to other peers.