And you cited something claiming trust in the medical system was 80% in 1973 and dropped to 39% in 2016, but I couldn't and you couldn't find the actual source of that 39% figure to find out what poll question(s) it was the result of. Without being able to see them, I suspect that the poll questions were different or were so vague that respondents' interpretations changed dramatically over 43 years.
61% might not trust the healthcare system in some sense; maybe they don't trust medical research studies, maybe they don't trust doctors to prescribe the lowest-cost effective treatment, maybe they don't trust that they can afford medical care, maybe they think the whole medical industry is conspiring to rip them off (approximately true). But I guarantee you if 100 people break their arms you'll see more than 39 of them in the ER. Same if they have the flu and the symptoms turn severe. Almost all of them will trust primary and ER care just fine, unless there are other considerations, and immigration status and fear of discovery is the most common consideration by far. One hears it constantly in immigration pieces on media like NPR.