Plenty of trained doctors do really stupid things every day.
As an aside, when I'm old and near death I was thinking of getting a doctor from India, which shouldn't be too hard to do. Then I'll have put on my grave marker, "Killed by Indians".
You will have lived a full life and been able to influence your end in such a way as to establish a fabulous punch line. I want the funeral that Georde had on ST:TNG.
A child has no such influence. That is part of the reason that a child's death is such a tragedy.