I was ambivalent about this until I got to the part where father and daughter had had previous discussions in which they agreed neither of them wanted to donate their organs, him because of his direct personal exposure to the process itself.

If the deceased patient had not wanted to donate her organs in the past, unless they had constructive proof that she had later changed her mind, it shouldn't have mattered whether either of her parents would consent to their donation.

If she had been registered as a donor by the time of her death, sure, the question of death becomes extremely relevant. But if she had not wanted to donate her organs, her organs ought not have been donated when she died, regardless of whether that happened before or after the hospital discontinued life support.