I'm confused as to where you got the idea that if people are terminally ill and chose to let nature take its course, it's not dying with dignity. Isn't the ability to die with dignity the ability to die a death you chose? I would think your family members DID die with dignity because they were able to harness the power of their faith to help them. Whether or not others believe in the power of that faith is irrelevant - it worked for them.
But, I do believe that denying the right for an more painless transition is wrong. While I do know occasionally miracles happen and the disease can turn around, those are the exceptions rather than the rule. I think the person just knows when there is no more hope and it's time to go. One of the questions I see a lot of these forums is about knowing when to put a beloved pet down and the answer is invariably - you'll know. One day the dog or cat will just look up at you and you know it's time to help them transition. When that time comes for a human, and as long as the person fully understands and agrees to what is about to happen, I don't see how it can be wrong. I would hope that I would be given that choice. Fortunately, when my mom passed from cancer, her passing was fairly quick and while she was in pain for a while, it was managable until the end. I am ever thankful for that.