@Linkat,
A correlation between hand washing and health isn't necessarily a measure of overall health. Probably some consistent (not constant) hand washing prevents some germs from colds and e.coli exposure. Basically, good habit...having a stronger immune system, good genes, moderate exercise and restfull sleep might determine better health.
On an interesting note after watching Ken Burns FDR biography on PBS, it was theorized that due to his isolation from the general public as a child and young adult, he may have not developed an immunity as did the general public to the disease that gave him polio.
"Eat a pound of dirt before you die"