A friend of mine from way, way back recently emailed me questions about the nice experts study and whether they provide any insight on findings regarding the Milgram study. I've pasted my response below.
The Milgram study (and similar ones) are much more focused on (a) diffusion of responsibility and (b) obedience --not necessarily perceptions of expertise and how they related to trustworthiness of informants in social learning situations. In Milgram's study, which of course didn't have enough participants (due to it having to be shut down) to run inferential statistics, they mostly reported exploratory and descriptive stats. What they have proposed, and others who have followed-up, is that people are more likely to engage in amoral tasks if they are being told to by someone else who seems to be an authority figure. This could be because (a) people have a tendency to be obedient to authority figures (i.e., Yale researchers in white lab coats), (b) they feel compelled to engage in the task because they had already agreed to do so and were being paid to participate (even though they were told--during the informed consent process-- that they would still get paid even if they chose to end the task early), or (c) in combination with the prior two reasons, participants may also feel like they are not personally responsible if someone else has ordered the amoral behavior, even if they are the ones "pulling the trigger" so to speak--this one has been used to explain some of the behavior by the nazi soldiers (which you referenced).
These types of research questions are slightly different than the ones that we were investigating, but could be related on a broader perspective--at least in terms of what characteristics make someone seem trustworthy (e.g., white lab coats? Ivy League affiliations?, High-ranking positions?). However, we are more concerned with two components of a learner's cognition:
(1) what features do children use to determine whether someone has knowledge; and
(2) are children more inclined to trust someone who has knowledge or someone who does not have knowledge but is socially-positive (i.e., nice).
Regarding the first, I've conducted research to examine what children understand about expertise. What does it mean to have expert knowledge and how much knowledge do you have (and about what) when you are labeled an expert. Then, I've looked at what cues children use to determine if someone has knowledge--are they labeled "smart", are they labeled "experts", have they demonstrated prior history of accuracy, have they exhibited nice behaviors? We've found that when children are asked whether someone has knowledge, they use BOTH information about that person's expertise as well as information about that person's niceness/meanness. Specifically, a nice person who is described as having no knowledge what so ever about a topic, is usually evaluated to have average knowledge (the half way point on a scale), where as a mean person without knowledge is usually evaluated to have 0 knowledge (the bottom of a scale). Then, when looking at both groups who are also described as having expertise, children move a nice expert up to the top of the scale and a mean expert to the midpoint. So a mean expert is seen as having similar amounts of knowledge as a nice non-expert. Thus, they are using niceness and meanness as well as expertise to evaluate whether someone has knowledge. In an interesting twist (or maybe not so interesting) children ONLY use niceness and meanness to predict someone's social behavior. So, a mean non-expert is seen as just as mean as a mean expert. Similarly, a nice expert is seen as just as nice as a nice non-expert. They don't get the same bump from expertise on niceness evaluations as they get from niceness on expertise evaluations.
Then, when it comes to trusting someone for information, Children prefer to ask the nice non-expert over the mean expert. This is not totally surprising considering children seem to rate them as having similar amounts of knowledge (even though they don't); thus, children are, instead, preferring the informant they have evaluated as nice (the nice non-expert) over the one who is mean (the mean expert). This is not a bad strategy on the children's part. After all, when trusting information that has been presented, it is important that you believe that the informant does not have the intent to deceive. If children predict that a mean informant would be more likely to deceive than a nice one (while still believing that they have equal knowledge), their best bet is to go with the nice non-expert.