I've finally managed to cancel My Health Record but no thanks to their pathetic, unworkable website. I ended up ringing the 1800 number which was helpful.
KittyKatKaper, I asked why I had a record and was told it originated from 01/06/16. So perhaps I was one of those that unknowingly took part in their trial? I'd have a lot more faith in government bureaucracies if they actually practised transparency.