Ancestral background can be determined by fingerprints

Indeed.

  > The contingency table (Table 6) shows that 20% (49)
  > of individuals classified as African Americans
  > [by their fingerprint model] are actually
  > European American and 22% (54) classified as European  
  > American are African American. In total 103 of 243 
  > individuals were misclassified for an estimated overall 
  > error rate of 42%. The area under the ROC curve is
  > 0.59, which does not meet the standard of a good
  > classification rule for a logistic regression of 0.90 
  > or higher.

From, doi:10.1002/ajpa.22869

They also mention in the discussion that even identical twins can have differences in their fingerprints, implying that uterine environment plays a role in defining fingerprint features. Given this, I wonder if it's not the case that some of the variance that they are ascribing to ancestry might actually be better explained by socioeconomic conditions.

This is Lewontin's Fallacy. Briefly, there is no contradiction between the existence of clusters and the notion that there is more variation within clusters than between clusters. For example, the variation in height within the categories "male" and "female" is greater than the variation between them (i.e., the difference in mean heights), but this does not negate the validity of the clusters "male" and "female". Indeed, only a small number of traits are needed to determine biological sex to high accuracy—e.g., height, skeletal density, cranial volume, waist-to-hip ratio, etc.—even though in every individual case the variation within traits exceeds the variation between traits [1].

Likewise, simply because the variation within sub-Saharan Africans is greater than the variation between them and other groups doesn't mean the cluster doesn't exist [2]. Indeed, it's easy to tell from a genetic analysis what percentage of a person's ancestry comes from each cluster, including sub-Saharan Africa [3].

The study in the OP indicates that fingerprints are like DNA in this regard. That doesn't mean the study is right, simply that it shouldn't be rejected based on Lewontin's Fallacy.

[1]: This is why anthropologists can reliably determine sex based even on fragmentary skeletons (such as "Lucy").

[2]: The edges of the clusters are often fuzzy, but again this doesn't negate their existence. The clusters "red" and "green" are fuzzy, too, but that doesn't make the categories meaningless.

[3]: For example, this is the premise behind Henry Louis Gates Jr.'s PBS show "Finding Your Roots" (http://www.pbs.org/wnet/finding-your-roots/). It is true that the label "African-American" is imprecise, as most African Americans have some European admixture, but typically over 70% of their ancestry is sub-Saharan African (http://isteve.blogspot.com/2013/02/henry-louis-gates-exactly...).