One does not need to have insurance to see a doctor. If you think about it, insurance is to protect one in the extreme situation. Hence, most of us paying insurance will get out of it less than we contribute. Only this way insurance companies can pay for the expensive care of the very few of us.
In other words, for most of us, most of the time, it is cheaper to pay outright for seeing a doctor, than buy health insurance. I do not believe that the person you write about could not spent a few hundred dollars to see a doctor and do basic tests. Then, if she was of limited financial abilities, she could use Medicaid.
Among family and friends, I can point at least a few instances of people who had good health insurance and were affluent enough to pay for the care they needed. But they died too early because they did not follow doctor’s orders, or simply acted recklessly. It seems to me that the person you write about fall in the same category.
Do you have any more convincing arguments for universal healthcare?