You can't state that falling occurs more often among men whose average age is 81. The rates are about the same, because men tend to fall more often than women. I don't know why, but there are more 81-year-old women than men among the general population, since women outlive men. That is a fact. Therefore, you cannot say that falling is more common among veterans. That is what I am having a hard time understanding.
The same goes for your statement that there is a higher risk factor for older veterans than for older adults. If you take a group of men with an average age of 81 years, they will all have the same risk factors and will all be subject to the same proportion of falls.