ABX itself is fine, but sense can very from person to person by a lot. The logical way to minimize the impact of variation is to carry out the ABX with a very large sampling population, preferable all different classes of the society from young to old and from casual listener to audiophiles alike.
Now, even if such an experiment can be carried out, the inherent nature of any scientific experiment is not to provide an absolute answer, but merely a explanation of what is closest to (or 'best fit') the truth as we know it. That explanation doesn't need to apply to every subject in the sampling population, it only needs to hold its water for the majority - that said, it doesn't mean those who are just right outside of the 95% or 99% significance must have invalid data, opinion, or sense. It only means the current set of explanation is not perfect enough to cover their part of the story.
There lies the biggest of all problem about ABX on small or individual scale - How do a person know which side of the bell curve he/she fits in? When a small group of subjects are measured, the standard of deviation can be way off the chart thus making the result / conclusion insignificant to the public. However, this doesn't in any way suggest that the obtained data is invalid (though the conclusion that drew from it might be). The data is always valid as long as the design of the experimental procedure is valid (that is, you are measuring what you want to measure and not something else).
Here we come full circle: Assuming everything else is the same, if a person is sensing 'A' from an object while the rest of the 9 person are sensing 'B', it doesn't mean the first person is wrong - it just means the first person's data doesn't fit into the group and doesn't support the theory you might have explaining why most of the group are getting a particular result. Do you think by telling the first person that his sense is not the same as the rest of the group, he must have sensed the wrong thing? That is definitely not the case since we already make sure they were all sensing the same object to begin with. 'A' is as real to the first person as is 'B' to the rest of the group. So if you tell the first person not to trust his / her sense because he / she is different, what is the point of the experiment? You could have just fixed up the answer at the first place.
Listening to music is not about finding the truth of the whole world, but only the truth about the listener. If you feel sad after listening to a piece of music, do you really need to make sure the rest of the world won't call you a fool because you get affected by some sound? Do you really need justification?