Double-blind means that the person administering the test doesn't know whether A is the compressed file and B the uncompressed or vice versa, and whether X is a copy of A or B.
Without a properly conducted test, users who want there to exist a difference between 320 kbps that they are able to hear will convince themselves that they can hear it.
But likewise, those who believe they shouldn't be able to hear any difference will convince themselves that they don't.
The A X B test eliminates this, because though you know that X is exactly the same article as A or B, you don't know which, and you don't know which of A and B is the higher fidelity one. If you believe that there is no audible difference, you can at best randomly guess at the identity of X. If a large number of subjects are tested and they all believe that A and B sound the same, the distribution of their identifications of X will be consistent with a random binary choice. If there are some subjects who can in fact tell the difference, that will show up in the data as bias toward the correct identification of X.
Those who think they have "golden ears" and convince themselves they can hear something they in fact cannot are called out by this test procedure, by their failure to actually identify X better than a random guess.