I suspect the opposite actually i.e. a decent number of people with Sky Sports will also have BT Sport, as the chances are people who have Sky Sports are interested in sport and of those a fair proportion will have it for EPL football. BT Sport shows exclusive Sport including EPL matches that aren't on Sky, so there is a lot of synergy there.
As for choosing BT over Sky again while I agree that is unlikely, there are some good reasons why some people might do this:
-BT Sport is free to BT Broadband customers, you have to pay for Sky Sports
-BT Sport can be had standalone/cheaper i.e. not need to pay a generic subscription in addition to the sport
-BT Sport only has a 1 month minimum term