 This is a costly oversight on Mackie’s part and the resultant disagreement can not be accounted for by the realm of non-moral fact.  The moral heretic in most cases would be someone who has developed an individual moral code separate from the conventional one.  A cereal killer would be the easiest example here but due to the involvement of insanity it would really only muddle and distract the argument on either side.  Instead I offer up the example of a criminal, nothing specific just your average run of the mill deviant the only stipulation being he isn’t committing crimes out of desperation. A criminal is immersed in the culture of whose laws he breaks, and yet he continues to break them.  Should his moral code not reflect the code of his relative culture? Why then does he defy the accepted or conventional moral rules? To use Mackie’s own reasoning, the best explanation here is moral disagreement; it is simpler and more likely to be the case. 
My ability to utilize Mackie’s own line or reasoning in this case, inference to the best explanation, illuminates another inconsistency within his argument. If the best explanation for disagreement within morality is that there is no objective moral value then wouldn’t it be the case that the best explanation of disagreement within moral code derived from culture is that morality is not culturally relevant? Why is it the case that the best explanation of disagreement is the refutation of the underlying premise in one case but not in the other?  If we were to follow his line of reasoning then there are two options that come to the surface concerning relative morals.  First is that we would have to conclude that the claim that morals are culturally relevant is false which would leave us without an adequate account of morality. This speaks to my major concern, the second option, that if we no longer have an account of morality that can survive the argument from disagreement inferring falsity as the best explanation then is inference to the best explanation a line of reasoning that can explain conclusively that there are no objective moral values? If used consistently it can not, and consistency is certainly required.
In response Mackie would most likely first argue that in the case of culture disagreement comes in the form of non-moral fact and there is no true moral disagreement, but I have already shown this not to be the case. He also could argue that objective value is a special case in which inference to the best explanation is the most accurate line of reasoning. Accomplishing this would be no small task but he could go about it two distinct ways, arguing that objective value is a special or dissimilar case in regard to relative moral beliefs or in regard to moral reformers and heretics. 