>Is this saying that veterans can kill themselves more easily because they have more rational clarity about the situation?
I don't think so. Doctors and veterinarians have an unusually high rate of suicide, partly because they have access to highly lethal means of suicide but also because they've become inured to mortality. For most people, the practical realities of death are somewhat foreign, which creates a psychological barrier between the urge to cease existing and the means of making that happen.
The vast majority of suicidal impulses are temporary; the vast majority of people who attempt suicide do not go on to die by suicide. While it is entirely believable that some people are afflicted with unbearable and intractable misery, that is certainly not true for most people who die by suicide.