Should the US military go on trial?

ITN journalist Terry Lloyd was shot and killed by US soldiers in 2003.

The US didn't didn't sign up to the ICCt when it was founded so it seems unlikely they will ever be tried there.

Should this kind of activity go unpunnished in a democratic society?

A soldier knows what he is there to do and firing upon civillians should never, ever be part of that.

Its not unprecedented for a US soldier to be prosecuted for their actions in wartime.

Is there any reason this should be an exception?