Measles is a highly contagious virus. It's been infecting, killing and causing severe complications like blindness in people with unprocessed diets for hundreds of years. It only relatively recently stopped doing that when we started vaccinating for it.
The immune system does its job fine on measles for kids and teens that eat that way everyday in the parts of the world where measles vaccination is widespread. It also does its job fine on the kids who have been vaccinated in areas where vaccination is not widespread.
Also consider before there was measles vaccination. Large deadly outbreaks were common all over the world in areas with vastly different diets and lifestyles.
This suggests that diet is unlikely to be a significant factor.
In that case I would also want to see their genetic details for reasons probably too taboo to speak of. But also what the kids are eating. I've seen their meals and while it's all natural I would not qualify all of it as healthy. There are a lot of bread and dairy and desert products. Kids will gravitate towards carbs and sweets. They make a lot of them.
Imagine realizing that you were not important-enough to vaccinate. Imagine asking why a sibling died, and the best your parents can say is that the kid died as a test and you gotta “be strong” and stick together.