You certainly do not need a valid SKY subscription to be able to recieve BT sport via a sky box. What you must have though is the SKY card which when there is no SKY subscription enables the SKY box to be used to view freesatfromSKY (which is not freesat) and if the card number is given to BT then BT sport can be viewed on the SKY box.
You do not have to be a BT Broadband/fibre customer to recieve BT sport via a SKY box ,but if not a customer then you would be charged.
thats a funny one bt sports trought sky but this must make your ky bill very huge
Nothing funny, it's here:
Free if you have BT broadband/fibre , if not you pay BT to recieve it through the SKY satellite service. You don't pay SKY at all