Maybe look at religious groups that strongly believe that sin causes disease?
In developed countries they just get treatment secretly.
Probably that's true for some of them, but it is likely not the case for many others. Part of the evidence otherwise is that there have been a variety of laws and court cases in the US about whether parents can refuse necessary medical care for their children. See for example here.
As everyone here knows, it would be a stupid idea to switch from airplanes to cars out of safety/terrorism concerns: Cars are a much more risky means of transportation than airplanes. But what other major risks are there that many people systematically undervalue or are not even consciously aware of?
The same can be asked for chances.