Somehow, I don't think the Pope's position adds anything to their legal arguments. I doubt they are basing their legal case on what the Pope said.
The problem with that, however, is that there are plenty of "devout" Catholics who are not lock-step with the Church on individual matters like use of barrier contraception and tubal ligation. This might've been one for her.
I've seen the videos and in my opinion her parents are projecting their wishes upon the harsh reality.