APA doesn’t have to:
Based on the cited APA rule, it appears to be true that APA does not have to justify its decision.
But as for the “You and I both know that isn’t the truth” comment (which was posted in response to a post reading “What more is there to say? They ‘played too good’ by some arbitrary APA standards, and the APA powers-that-be booted them out of the tournament”), it isn’t holding up too well. The APA’s own rule says that its determinations regarding true playing ability as compared to participating skill level are “necessarily subjective” and can be made in its absolute discretion (i.e., can be arbitrary), and it says that if it decides there is a difference between true playing ability and participating skill level, it can disqualify a player (i.e., boot them out). Sure seems like truth to me.