Story 2: Mr. good parent pushes his 4-year-old son to the ground and out of the way of a moving vehicle. The son scrapes his elbow and bangs his head. After a trip to the emergency room finds that the son will be fine, the child, too young to understand what happened, wonders, "why would daddy do this?" Although the incident resulted in no physical trauma to the child's head, the psychological trauma takes a toll. The child goes on to get fewer years of education, receives a lower income and is more likely to end up in prison.
Story 1 is far more believable than story 2, but upon reflection, there's no reason it should be. The two incidents are identical in regard to the child's perception. Psychological trauma can't come directly from the motives of the parent without first passing through the child's interpretation.
I started thinking about this immediately after holding my screaming child down so a doctor can thrust a needle into his arm. My child had no idea whether we were doing this because vaccines prevent dangerous disease, or if we were doing it for fun. If we were doing it for fun then it would be a lot more believable that this traumatic experience changes him forever. But if we were doing it because vaccines are important, then it's much more believable that this traumatic experience will wear off, be forgotten, and won't do any psychological harm. But again, in regard to how the child interprets these situations, they're exactly the same. The probability that one causes psychological harm should be the same as the other.
I think this is because humans are biased in thinking that good intentions lead to good outcomes. Behavior enacted for virtuous reasons leads to good results, even if it's the same behavior enacted for sinful reasons. This is why some parents believe that to spank is less likely to have bad long-term effects if it's done to correct bad behavior rather than because the parent is mad at the child. In reality, a lot of the bad behavior of children also piss parents off, so the parent could be spanking for any combination of those two motives, and the child could interpret it as any combination of these two motives.
Whether it's vaccines, spanking, pushing your child out of the way of a moving vehicle, cleaning cuts and wounds with hydrogen peroxide, and some other example, parents understand that sometimes you have to put your young child through short-term pain for long-term gain. Adults can argue about how any particular example might be right or wrong, but the child certainly doesn't know which is which. This means that if short-term pain causes long-term psychological trauma, it should be true regardless of whether that short-term pain was necessary.