I love the rational of not wanting to get medical treatment there, because the doctors locally wouldn't have known about her "extensive medical history," because as we all know, the internet doesn't exist in Hungary, nor do phones or faxes, so communication with the state-side Dr. would have been impossible.
If I have a reasonable choice, I obviously want my primary care Dr. treating me, but here is a great example of a recent experience I had with a Dr. at an "Urgent Care" center:
I was a day away from leaving on a work trip and developed a rash on my upper body, for unknown reasons. It was after hours for my Dr., so I went to a local Urgent Care center. I explained to the Dr. there that I was concerned and hoped to have some kind of results before my trip, since I would be away from home, and his response was "While I understand your concern, the doctors there would have just as much knowledge about you as I do."
It was a good point, that even if she had to go to an ER state-side, the doctors wouldn't know her any better (until her Dr. came in/called). Refusing treatment is what lead to her death, not being rejected transit that wasn't possible.