The YouTube API will return all Liked videos that are public or unlisted. It will not return private videos. However, the total number of videos within the playlist, pageInfo.totalResults will be the summation of public, unlisted, and private videos as far as I am aware. Maybe let the user know that some of the videos in the playlist is private, hence the inaccurate number.
For example, in my case there is 520 videos in my Liked playlist, but only 490 are currently showing.