Remember they wanted to shove her into a throne and even when that failed she is one of the strongest women in the Tower. And we've seen any number of times that the tradition of staying out of each others business is pretty weak in actual practice. Elaida had no problem trying to interfere with Moiraine, Verin didn't seem too suspicious to Siuan and Moiraine when she butted in, there are other examples throughout as well. But the Hall and the Tower in general are not held to that tradition in any case. They are a governing body not a couple of AS randomly meeting up outside of the Tower.

I do think you are correct regarding the BA taking notice. I'm just surprised it took 20 years!