It certainly includes training sessions and events run by BHDTA carriage driving but it isn't very clear in the rest of the text about non event driving as it refers to riding.
I would ring BHS, or better email them so that they have to reply in writing and you can keep the reply as a record.
Try to ignore the annoyingly disinterested tone you often get when ringing (even when you are giving them money by renewing membership)....:-DD