Cannot comment on the core of your post, but remember that unless the WP is coded in your database as a 'flyover' an FMC will turn early with a turn of 130 degrees for the next track. This is a very common problem with those who insist on LNAV handling for complicated and close-in turns.
HD - I think FD is right! The a/c 'interrogates' the station and the distance is measured on response return time.