"It was Sternberg and not the BSW who assigned the peer reviewers."
And Sternberg was the BSW's managing editor. Thus, the BSW. That's what a managing editor does.
Berlinski suggests there was a board of editors involved, and the BSW's statement states that an associate editor would normally be involved in the editorial process; but Sternberg took an editorial short-cut and worked alone. Obviously Sternberg involved no one else from the BSW in the process because he knew that the article would be as unfavorably received as it was in the BSW's post-publication statement. Sternberg clearly abused the trust of the BSW; and it is misleading to say that the BSW appointed the reviewers, it was creationist-affliliated Sternberg. Sternberg does argue on his blog that he had the authority to make any editorial decisions, but the BSW said in its statement that this authority was used inappropriately.