Hi Helen,
another person who doesn't quite know how to use insert..
My thoughts followed a similar path. It could well be that the author originally put "..a horribly wrong turn", and the editor found this too strong - and amended it without considering the result in context. For me, "a badly wrong turn" sounds awkward because the word "badly" contributes nothing here. It is too weak to reinforce the message. It is akin to a pleonasm, if you come to think of it.