You are of course correct, and Carter has no idea what he is talking about.
Casualties:
Rev. War 80 months 4,435 deaths 55/month
Civil War 48 months 558,052 deaths 3,846/month
WWI 19 months 116,708 deaths 2,816/month
WWII 44 months 407,316 deaths 6,639/month
Vietnam War 90 months 58,168 deaths 526/month
Iraq War 20 month 1,067 deaths 53/month
You can go here to verify figures and compare combat casualties to non-combat/theater deaths.