Comapring family history and DNA for assessing disease risk

An article Comparison of Family History and SNPs for Predicting Risk of Complex Disease in PLOS Genetics. The abstract states that:

..family history is most useful for highly common, heritable conditions (e.g., coronary artery disease), where it explains roughly 20%–30% of disease heritability, on par with the most successful SNP (genetic) models based on associations discovered to date. In contrast, we find that for diseases of moderate or low frequency (e.g., Crohn disease) family history accounts for less than 4% of disease heritability, substantially lagging behind SNPs in almost all cases. 

In the body of the article that conclusion is made more explicit:

current SNP-based risk models outperform complete family history for 13 out of 23 conditions and outperform restricted family history (where not all information is known) for 16 out of 23 conditions, with the magnitude of the differences in performance greatest for diseases of low frequency.

However, it's not an either or proposition:

...comparisons of family history and SNP-based methods aimed at declaring one method categorically superior to the other create a false dichotomy: in general, there is no need to choose between family history and genetic risk profiling. An understanding of both types of information would allow us to obtain a better picture of an individual's potential future health. 

While this study examines the impact of having incomplete family history health information it does not examine the situation where such information is erroneous.