The problem that I see, is that if you accept the OP’s precedent (or that of any of the many posters in this thread who are positing similar punishments on the parents in the OP’s scenario, or laws to prevent that scenario) the question then becomes to me, what recourse does a family have when they believe, rightly or wrongly, that the so-called scientific medicine they are recieving is harming their child?
I’m a mental health consumer, so I tend to view any kind of corner case scenario through the lens of how it might deal with some real world examples of psychological treatments. In the past several years, there have been studies showing a link between the use of anti-depressants and increased suicides with teenagers*. For that matter, the extent to which licensed and regulated professionals are willing to prescribe things like Ritalin and other ADD medications, often in spite of reports of disturbing side-effects, leaves me firmly of the opinion that there are a number of times that parents should retain the right to reject the advised course of treatment.
The sorts of laws that some posters have advocated in this thread would have the effect, I believe, of leaving parents at the mercy of medical professionals who can often end up with severe cases of tunnel vision. (Note: I’m not trying to accuse anyone of improper motives.) FTM, there have been a number of cases where medical professionals have advocated prosecutions for SIDS deaths, sometimes to the point of ignoring evidence of other potential explainations, which already leaves many parents worried**. I know that such events are corner cases of extreme magnitudes, but that doesn’t mitigate the chilling effect for some people. I tend to believe that the average person, if they’re aware of such cases at all, has only seen the more sensationalized versions of the news, and lack the background to sufficiently understand how unlikely such things are.
Finally, I think that this modification of Randi’s central thesis is key: if the State is willing to support homeopathy as a legitimate means to treat disease, the bar for proving negligence, let alone murder, has been raised very, very high. Any argument that begins with the reasoning that homeopathy is at best a harmless crock of nonsense, so the parents should have known better than to risk their child’s health on it is going to be doomed to failure, given the apparent support it recieves from the gov’t. As other posters have suggested, I believe that murder is going to be flat out impossible to prove. Negligent homicide will be hard enough, and will turn, I suspect, on how much time the family had to recognize that what they were using wasn’t working, and to consider getting their child treatment.
*There is a link on the NPR page linked that goes to the FDA’s .pdf about the study.
**I wish to state that while I recognize the huge potential for abuse with diagnoses of Factitious Syndrome by Proxy (aka Munchausen’s Syndrome by Proxy), I am vehemently in disagreement with the thesis of groups, such as MAMA: that all such diagnoses are conspiracies by the medical establishment to cover-up their own failures and lack of understanding. Factitious Syndrome by Proxy does exist, and removing the diagnosis will do nothing to improve safety, nor medical care, for the public, nor at-risk populations.