Yes, it was "her" (BASSA's) right to take BA to court.
However with all these things, you don't do it on a whim or in a fit of pique. You do it based upon considered research and an examination of all the options, especially the one which says "court cases can also be lost".
The BASSA case was always going to be tenuous and I'm damned sure if someone took me to court, lost and cost me a fortune, I'd be looking for restitution. I'd also want to make sure that person could not do it to me again if the mood so took them.
IMHO, I expect her to retire quietly to California in the next few months.