Pretty much only DNA analysis rises above shamanism,[1] and juries and judges have incorrect perceptions about the accuracy of those tests. While the often-quoted false random match probability is astronomically low, that error rate is dominated by lab error, which can rise to 1-2%.
As an aside, the Innocence Project has a better description of the details of what happened: http://www.innocenceproject.org/cases-false-imprisonment/kir...
[1] See also: http://lst.law.asu.edu/FS09/pdfs/Koehler4_3.pdf.