What AR states that a Soldier cannot attend BLC if they have been barred to continued service or re-enlistment?

It's directly in the Promotion regulation and the Retention regulation which talks about the bar. It says the Soldier will be placed in a non promotable status while barred. STEP program says that the Soldier first becomes promotable then attends NCOES.

But all of that is really irrelevant because once a Soldier is dropped from NCOES it takes an approval from their Division Commander to get approved for a new class date. Commanders have nothing to do with getting class seats.

You are an AD SPC promotable, why are you asking a question here that you should already know the answer to through a basic regulations search, a google search, or talking to and with a retention and training NCO?

As to your situation with your soldier, your commander should know this answer as they are a command grade officer. He or she did not place the bar, that was done when the SM lied, and then dropped the course. By your description she is lucky there were not charges brought up on her for her actions. Her bar can be lifted, its just a matter of if command deems the SM is worth that effort or a second chance to attend BLC. I mean they pulled this crap once, what says she will not pull it again and really have they actually learned their lesson or are they the same crap bag they were?