She didn't necessarily have to share it with Quinta as the two people she shared it with could have shared it with her. Quinta's name is just being brought up as it's her name that's attached as EP. That type of situation happens more often people think where scripts and ideas get passed around from people to people and eventually end up in TV/Movie creation. It happens in the entertainment world all the time.
If she can prove that her original script eventually ended up in the hands of ABC/Quinta she has a valid case.
I know that part, but if she submitted a script, she would have to prove that the script made it to the hands of the suits at the Mouse, and to Quinta, and that it was indeed her script. That's tricky to prove. Then we have the whole possibility that her script was sold by her to said people to make it to the Mouse suits.
Plus, Networks usually pass scripts off to a proven creator, not a relatively unknown.