Well, to be honest, even I don't know how they decided that the justice was biased or not, but even forgetting the bias part, if they felt he was not competent enough and was making mistakes, they could still raise a stink.
And yes, threatening to walk out was cheap, esp. after the neutral judge was appointed. But again I ask, if the Indians felt that, with the evidences and stuff available to them, there was no way any adjudicator in the world could indict Harbhajan, then surely, in that scenario, they can say with confidence that IF Harbhajan still gets indicted, it is surely injustice and therefore, they will walk out????? Again, I am not saying BCCI acted on these lines of thought, but there is still a possibility??? Although, I guess the probability of it basically depends on the person's mind....