Are Lawrence Kohlberg's stages of moral development supported by empirical evidence?
Kohlberg constucted his stages of moral development using a sample consisting of 72 boys from Chicago. The sample consisted of three age groups: 10, 13 and 16 years. This was also the start for a 30-year long lasting longitudinal study to test his theory (Colby, Kohlberg, Gibbs &amp; Lieberman, 1983). The results generally support the theory. Younger children are classified as belonging to the lower stages, older children as belonging to the higher stages of moral development. Differences between stages become smaller as one goes up the hierarchy. Also, age differences between stages become smaller with higher stages.

But there also appears to be some criticism. First, there were only few subjects in some of the age groups of the study. Second, apparently Kohlberg has quite often revised his theory and reformulated the descriptions for the stages, and it is not always clear which version was used for testing. Some critics have therefore argued that Kohlberg has "immunized" his theory against falsification. This point also has to do with criticism regarding the assesment of the moral stage, which was done using the Standard Issue Moral Judgement Test, an interview developed by Kohlberg. 

Everything I have said so far is taken from Heidbrink (1991), who has tested the theory using a different test, the Morals Judgment Test by Lind. His study supports Kohlbergs's stages. Among over 1000 subjects between ages 14-29, only two showed a pattern that is not consistent with the theory.

In a re-analysis of a study from 1913 – 45 years before Kohlberg's first relevant publication and thus free of the suspicion of having jumped on the "Kohlberg bandwagon" –, Heidbrink (1989) finds that the results conform to those of Colby &amp; Kohlberg's longitudinal study (1987). He concludes that the fact that American adolescents of the 1950s and 60s show the same moral development as pupils from Berlin before the First World War supports Kohlberg's hypothesis of the universal validity of his stages of moral development.

If you want to go further, the Wikipedia article on Kohlberg's stages has a long list of references that you can look at. Probably some of those review the relevant research. Also try to input Kohlberg's own articles or books into Google Scholar and click the "Cited by" link to see which other articles deal with this theory, there will be empirical studies among those.

After collecting all the information to answer your question, I have to say that I am also a bit surprised about the example chosen to describe stage one. The example caters to very young children, while youngest boys in Kohlberg's study were 10 years old. Maybe we shouldn't focus too much on this example. Right off the bat I don't have a better example, but I could imagine there is one. 

References: 

I used German publications. If someone has English references, please help me out here.


Colby, A., Kohlberg, L., Gibbs, J., &amp; Lieberman, M. (1983). A longitudinal study of moral judgment. Monographs of the Society for Research in Child Development, 48 (Serial No. 200), 1-124. University of Chicago Press.
Heidbrink, H. (1989). Moralpsychologie: Die Reanalyse einer Untersuchung von 1913. Geschichte der Psychologie, 6, 4-9. Available online at http://journals.zpid.de/index.php/GdP/article/view/424/459
Heidbrink, H., &amp; Lück, H. E. (1991). Stufen der Moral: Zur Gültigkeit der kognitiven Entwicklungstheorie Lawrence Kohlbergs. Quintessenz-Verl.