Yes, setting the following script works for me and will show the my_rating tag in the bottom list for tracks that have a rating:
Works also when loading the track you linked above as a non-album-track into Picard. What happens when you right click on a track? Does it show the rating stars filled up?
EDIT: I think I know what causes the issue Picard only uses your personal ratings, not community ratings. So if you have not rated a track yourself it will not add the ratings to the tags (you can however set the rating in Picard, and it also rate on musicbrainz.org). The idea was that a rating is a very personal view, and the fact that I find a certain song amazing probably has not much meaning to you. But having the option to use the community rating makes sense, of course.