Protocols exist for a reason - to protect you, your agency, your patients, your community, and so on. Parents have the right to make healthcare decisions for their children, just as they have the right to hold religious beliefs you and I might characterize as insane, stupid, etc etc. You don't get to take those rights away, and not only because people who were elected have passed laws and people who were appointed have written SOPs that say so, but also for larger, ethical reasons. Who are you to say what they are doing is incorrect? You approach the situation as a healthcare provider and you want to provide care, but your priorities are only one facet of the situation. The parents (in this made-up scenario) have priorities stemming from their religious beliefs. You are going to decide that your beliefs trump theirs when it pertains to their child? That's arrogant.
Who am I (and who are you, too)? I'm an educated medical professional, acting in place of a physician, and I'm rendering my educated medical opinion that the child in front of me is likely to die or be disabled if they fail to receive immediate care. Our society says that children dying is "incorrect," and in this case we are the voice of society. Its not an arrogant personal decision, its a societal decision that is necessary because children are generally unable to protect themselves from insane/stupid/abusive/foolish parents.
I don't really understand the basis of your opinion either. I doubt it came from your training. Nor does it seem to be based in the law. Did you read the rest of the thread? If not, read it, and read some of these too:
http://pediatrics.aappublications.org/content/128/2/427.full.pdf
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2528596/
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1726617/pdf/v022p00869.pdf
http://www.ncmedicaljournal.com/wp-content/uploads/NCMJ/sep-oct-07/brezina.pdf
I'll admit that there have been minimal test cases so the issue is a little complicated. Additionally rules may change a bit state to state, but in general it seems pretty clear that the courts have held that the state has a substantial interest in protecting the lives of children, and that the state's interest outweighs the parental interests in exercising control over their children. Parents have rights, but so do children. In this case, the child has the right to grow to adulthood and make their own stupid decisions. TLDR:
parents are non-omnipotent; they do not have the right to decide if their child lives or dies.
I don't' really see how this is very hard - what would you do if you saw a parent beating their children with a whip and claim its was religious practice? In the process of sacrificing them at an alter? If you say "walk away" or "watch until PD arrives" I think I would question either your honesty or your integrity. This is little different - a parent attempting to cause the death or injury of their child, the reason is irrelevant.
Obviously making contact with medical control ASAP, trying persuasion first (but quickly) and getting PD and supervisors to back you up absolutely ASAP is critical. This scenario will likely never play out the way it is described. But if it did, I have trouble respecting any person who would truly watch a child die, knowing they could help, due to fear of legal repercussions (which are doubtful anyways).
This reminds me of all the times people spout nonsense about how EMS is "just another job." If you feel better by refusing to take accept the importance of the decisions you are paid to make every day, great, but that doesn't make you a Toyota technician. Practicing medicine (even via protocols)sometimes requires tough decisions and can have a profound impact on people's lives. That requires some moral fortitude (and, of course, a working knowledge of your states laws and policies etc.) - you can't always just punt responsibility.