The Power of Christ Compels You...To Do Nothing?

This is something that, like many things in religion, defies all logic. 'Faith Healing is the attempt to use religious or spiritual means such as prayer, mental practices, spiritual insights, or other techniques to prevent illness, cure disease, or improve health.' (Thanks, Wikipedia) Basically, if you get sick, in some extreme (but disturbingly more frequent) cases someone prays for you to get better, instead of relying upon modern medicine, or any, for that matter.
There are several recent examples (2) (3) of this going terribly wrong, where the child being 'faith healed' has died, sometimes from easily treatable maladies. Several parents have been or are currently being prosecuted for the preventable death of their children, a bit of insult upon a self-inflicted injury.
Growing up in the LDS Church, I've had my own experiences with this type of treatment, although no so radical. It is called a 'spiritual blessing,' preformed by men who have the 'priesthood' and is meant to speed up or end an affliction. I was in a bad bicycle accident at the age of 15, and received a broken elbow and collarbone, among other injuries. This was a year after I had been hit by a car on the same bike, from which I received a mild concussion. In both instances, my parents and those around me had the sense to send me to a hospital, and save the blessings for after I was taken care of medically.
Although I no longer believe that spirituality had anything to do with my subsequent recovery and quickly healing bones, I still believe there is some effect in this practice, as more of a psychological and physiological placebo. The human body is an amazing thing, and this mental placebo effect my or may not speed up recovery from an illness or injury, but it is still widely noted and based on scientific fact, not religious faith.
The other part of this 'faith healing' explanation is something the Romans had a phrase for, long before Christians were around. Post hoc ergo propter hoc is basically the idea that a remission or sudden reversal of an illness happens simultaneously, but independent from anything a faith healer has done. You just get better all on your own, whether you are prayed over or not.
So should these blinded and misguided people receive jail time for letting their kids die instead of being proactive? I'm actually still on the fence about this one. On the one hand, they are practicing what they believe is their religious right (however archaic and ill-informed) to not rely on medical help. But, when the life of someone else, particularly a child hangs precariously between faith and medicine, should a prayer be your only response? Shouldn't someone take the blame and be held accountable?
God has been particularly hard to track down and has not released any statements as to his involvement in these tragedies.