I appreciate having a forum such as this to investigate this timely topic. While there are no easy answers, it occurs to me that once again this is an issue where one has to be mindful of one's intentions, actions, and the possible consequences of those actions. So many factors enter in to such a decision.
Even examining it at another level, some refuse to end the suffering of our sweet animal friends. It is difficult for me to reconcile compassion and not killing when that suffering is intense and seems to be a cruelty to allow it to continue.
The above woman's father who asked for his gun was making his intention clear, but he seems not to have been clear about the repercussions for his beloved family. On the one hand using his gun may have seemed brave, on the other, an infliction of other needless suffering on others, WITHOUT regard for the impact of his request on their lives, which could well have inflicted much more and longer suffering than what he intended to avoid.

I have the idea that should I be dying that the generous thing in fact to do would be to get complete with my earthly duties, and just step right into death, not wasting resources, not prolonging the inevitable, and acknowledging that my time had come to go on.

Could I do that for a parent? IF I were clear that my parent was resolved, clear-minded, needed relief, and if I felt in my heart that it was the compassionate thing to do, I would likely be a yes. But then that situation is not immediate, and theory is easy to postulate vs. facing an emotionally exacting and spiritually challenging decision.