I've had Bsd and to me they don't even come close.. there was very strong tendency to have a lot of white at the base of feathers on all Bsd, even on the 'darkest' birds. The birds are too dark, and the tails are way solid to be Bsd. Even that rooster does not look Bsd to me- too much color in tail.

Those birds below were bred by me, they were on black(don't know if E or ER)and nothing else. Notice how much white each feather on the hen has. Tail almost half white etc.

Personally, the birds in the first post look to have autosomal barring pattern. I suppose if you really want to settle this, breed that rooster to a black hen. If it's Bsd, it should be extremely obvious.