For each request sent, the tracker returns random peers at a limited number. For instance, if there are 1000 peers in the swarm and the tracker sends only 20 peers for each request, there must be at least 50 requests sent to know every peer in the swarm
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.