There is a fairly huge debate going on (and has been, for the past couple years) over whether US Army medevac helicopters should be painted with distinctive GC insignia (red crosses) and armed.
In 2003-2004, in Iraq, I flew on some medevac helicopters (I was helping the air ambulance guys set up satellite communications at their remote locations, so we used a medevac helicopter to fly to the locations...was pretty awesome). They had...M9 9mm pistols. Something is wrong when the civilian has a better weapon than you do in a war zone. Later in 2004, they got M4s as well.
USMC and USAF don't mount GC insignia, and have .50bmg machine guns, miniguns, etc. on their aircraft. i.e. a USMC or USAF medevac aircraft is better armed than regular USA blackhawks (which just have a couple 7.62mm machineguns on the side).
As a result of not being armed, medevacs became great targets. They were also no longer allowed to fly single-ship missions, increasing the risk (with one helicopter, flying 50-300' AGL, you're pretty much out of range by the time anyone notices you and is set up to fire. With two, the guy in back is doomed.)
The stopgap was to require an Apache gunship escort for every unarmed blackhawk mission into a dangerous pickup. It turns out a lot of the time when someone is shot and seriously wounded on the battlefield, the area is dangerous. The medevac guys could be in the air in 5-15 minutes, but it often took a lot longer for the Apaches to be ready (since they weren't dedicated, and might actually be busy fighting a war, plus they're less reliable aircraft). Pretty much the only luck was when there was an Apache already in the air for another purpose, which would often be willing to divert to help save someone (often, enemy or civilians -- plenty of times when little kids in car accidents technically not even US responsibility would get medevaced back to a US base for top-tier medical care, and in a few cases, months of free burn/etc. rehab due to a cooking fire or car accident)
Essentially, the faster you get someone from injury to surgery, the greater the chances for both immediate survival and long-term good outcomes (not losing eyesight, limbs, etc.). The "standard" is one hour, but obviously 30 minutes is better than 59 minutes, and 59 minutes isn't much different from 1h01m.
By requiring an Apache escort for most combat medevacs, they extended the time needed to pick up patients. This statistically cost lives, limbs, and eyesight, but can be fairly clearly tied to some specific deaths as well, where a blackhawk was able to get there in 15 min, but was held due to lack of an Apache for another 45 minutes.
There are arguments from the US Army medical side that arming helicopters is illegal (but, removing the crosses and arming them is fine). The best theory for why they resist is institutional inertia and fear that if they start arming medevac blackhawks like regular troop transports, they'll lose operational control of the aircraft eventually (because, hey, it's another helicopter available...). IMO there's no chance this would affect their 2-3 aircraft on rotation for active medevac calls, but would potentially remove their extra aircraft for moving their own personnel (and commanders) around.
Also, some of the medics I knew were pretty badass soldiers (especially on the SF side). In Army SF, it seemed pretty clear that the medical/communications guys were generally smarter than the weapons/demo guys, and that all of them met a very high standard for regular combat skills. 160th SOAR (the special operations aviation unit) recruits pilots pretty heavily from medevac, too, since the medevac pilots would be willing to fly in the worst weather, the most difficult landing areas, etc. The Air Force's version of medevac medics, pararescuemen, are one of the major parts of their special operations capability, basically like SEALs or Delta but also happen to be paramedics.