One of the things I've learned is to apply the Socratic method, preferably in front of their colleagues if they try to brush you off. Also, if you've got scary symptoms, demand they write down what your symptoms are on your record and why they aren't concerned, then demand a copy of all relevant records (it's your property) -- this often gets them to reevaluate your risk in terms of their career.
Worst case scenario, you can make up medical history. I had a family member pass recently from colorectal cancer. They had symptoms but their PCP kept insisting they were too young. My family member suddenly "remembered" her aunt died of CRC when she was a kid. This got her referred to a gastroenterologist, and they found out she was stage 4...after her PCP delayed her diagnosis for like a year. She actually had grounds for a malpractice suit but who's got the energy or money for that when they're fighting stage 4 cancer?
Also, know your state's agency responsible for policing health insurance. This family member's insurance company routinely tried to deny life saving procedures, but a call to the right govt agency set them in line each time.
Here in Mexico, i can get to doctoralia and make an appointment with a high specialist , like a Vascular Neurosurgeon. All by myself. The first visit will to maybe $200 usd (and that's very high) and normally it's a week away at most. No waiting on the private health option.
Of course if you go with public health, it's a disaster and a shame.
The advantage of the less developed countries is that you can get pretty good private medical care for a reasonably price. The quality may not match the very best care available in the rich countries, but in many cases, it is adequate.
What is a "reasonable price"? Relative to a rich country, the price may be low. But relative to the average income to common folks in that country it is likely just as expensive as a comparable private option is in a rich country. Apples vs. oranges.
Iow, you are describing the perspective of a rich person in a poor country. I don't think a rich person in the U.S. (top 0.1 percentile, let's say) minds the health case costs in the U.S. either.
Of course the top tier private hospital and specialists can be pretty expensive, but is not that expensive to avoid the public/government health system.
> Doctors are used to nuts who googled the symptoms
When you were there, did you have anything else to come with than the symptoms of your family member? In other words, how did you look different to the doctor than somebody who just googled their symptoms? (Or, to put it differently, without meaning disrespect, in which way were actually different from cases you referred to in the above quote?)