All videos are private unless you share your video's link with others and/or post it elsewhere. The end of the link contains a random selection of characters, which is hidden from search engines and can't be guessed. That means no one can stumble across, search for, or access your video without your permission.
Downloads are only available to the owner of the account. When you share a link to your video, the viewer is only able to stream a copy. That means your video won't be available to view if you delete it off of your My Videos page.
Users on the Professional or Teams plans can also hide the branding from your shared links so your viewers are taken to a totally unbranded playback page. If you remove the branding from your video, your viewers will have no way of knowing where the video was created or where it's hosted.
For more information, check out, Share your video without Animoto branding