It might be “60p”, not “60hz”. This is the media source problem. The media source is encoded in “60p” or “24p” for movies. When you play Bluray, it will show “60p” for the preview or other advertise, but it will switch to “24p” when the movie starts, since the movie was taken and encoded in 24 frames per sec.
TV is refreshing the screen with 120hz frequency based on this frames per sec. The faster refreshing, the clearer (less blur) the image is, but 120hz is already enough for most viewers.