I have run in to this several times. The policy is written ambiguously, leading to multiple possible interpretations. Because A-List + companion boarding positions are assigned 36 hours in advance of the flight, you won't get an A with a same day change and they won't let your companion board with you after A.

Like I said, it's a badly written rule but that's the interpretation most gate agents seem to follow. I still try to board with my wife after A but most of the time they make her wait.