Visitors do die within National Parks. Here is my tabulation for fatalities over the past couple of weeks, taken from the NPS Morning Report:

Twelve total fatalities - 3 in a plane crash, 1 suicide, 2 in motor vehicle accidents, 4 drownings, 2 falls (one while mountaineering). Also reported was successful use of bear spray by a NPS employee. This is a small sample, but I believe it is fairly representative. Falls and drownings are the preeminent hazards to visitors, year after year.