The API can toggle a video’s privacy settings, but cannot be used to allow video playback outside of the privacy settings we provide. Learn how at Vimeo Developer: Interacting with Videos.
For example, you can use the API to set a video as password-protected and set the video's password, however, you cannot use the API to authenticate and bypass password protection and allow playback.
Learn more about Vimeo's video privacy settings at 'Overview of video privacy settings'.