It's possible that one of the twins deliberately tied the Langford double knot, knowing Julia won't be able to break free from it in time, in order to sabotage Angier's act and eliminate the business competition - so that the only great magicians remaining in town would be the Borden brothers.
This ruthlessness in business, this willingness to sacrifice both human and animal life for the sake of fame and profit, is paralleled both in the story of Edison's men destroying the fruits of Tesla's hard work, and thus eliminating the competition, and in Angier's own story of destroying himself by drowning, over and over in agony, for the sake of putting on a sensational show. If these men were willing to sacrifice the lives of beautiful birds, their fingers, the happiness of their romantic partners, their own happiness, and even their own lives to sabotage each other's acts and prove the more successful in this business of creating illusions, why wouldn't at least one of the Bordens have it in him to sacrifice the life of an innocent and beautiful woman and the happiness of his business rival in order to nip his competition's success in the bud and come out on top.
Maybe this Borden was a plant from the start, wishing to work with Angier in order to ruin him, just as Olivia was a plant sent to work with Borden in order to ruin him. Maybe he tied the wrong intentionally, after having tested it on his own and determined that it is not possible for anyone to wiggle out of it in time, and maybe he convinced Julia beforehand to be daring and not to protest when he ties it. We can't discount this possibility. This whole movie is about the ruthlessness of business, about how vicious people can become towards one another and how cruel even towards their own selves when they value business success, fame and profit more than life itself.