I find it odd that no one has referred to the fairly recent thread discussing the WPBA's position on the issue.
http://forums.azbilliards.com/showthread.php?t=429214&highlight=wpba+transgender
In that thread, it was pointed out that a transgender player (Annie O) played for years on the tour and Rhea pointed out the specific policy the WPBA has on the issue (under that policy, simply identifying as a woman does not satisfy the requirement, but they look for a note from a doctor that the persons hormones are within the medically acceptable range for a female). So if Norma had tried to compete at a WPBA event, there would be a set of rules to determine whether that was permitted. One can obviously debate whether the WPBA policy is the right one, but at least they have a policy.
On the very narrow question of what happened with this player (or should happen) the issue to me is whether the APA has a policy on who it allows in the woman's division. They might have a policy like the WPBA, or they might have a different policy.
In this day and age, the APA (and every league) really should have a policy, and it should be communicated to players and league operators.