To be left holding the baby means to be made responsible for a problem that nobody else wants to deal with, but the sentence states that they will not have to deal with any negative consequences
Consider the statement "The media will make them responsible for the problem and they will not have to deal with any negative consequences.". Based on this "The media will pass the buck to them and they will be left holding the baby." a true statement? Yes, no, or I don't know?