Bad reference VS no reference
The bad reference is given to prevent you getting the position, it is a warning to whoever might supervise you. From what I have seen, it is quite common for far more subtle and hidden negative messages to be put into an academic reference than what you have described. In these cases the references are not used because the letters are there to convey a warning. That's not to say I know the right answer, but my feeling is that a bad reference gives you no chance whereas a single good reference gives you at least a shot.