In a recent paper published in PNAS (Golan et al. 2014), residual maximum likelihood (REML) seriously underestimated genetic variance explained by genomewide single nucleotide polymorphism when using a case-control design. It was concluded that Haseman–Elston regression (denoted as PCGC in their paper) should be used instead of REML. Their conclusions were based on results from simplified linkage equilibrium SNP simulation (SLES), which the authors acknowledged may be unrealistic. We found that their simulation, SLES, unrealistically inflated the correlation between the eigenvectors of the genomic relationship matrix and disease status to values that are rarely observed in real data analyses. With a more realistic simulation that the authors failed to carry out (as they noted in their paper), we showed that there was no such inflated correlation between the eigenvectors of the genomic relationship matrix and disease status. Because REML uses the eigensystem of covariance structure, the inflated correlation artefactually constrained its estimates. We compared SNP-heritabilities from SLES and a more realistic simulation, showing that there was a substantial difference between the REML estimates from the two simulation strategies. Finally, we presented that there was no difference between REML and PCGC in real data analyses. This pattern from real data results differed strikingly from the pattern in the simulation study of Golan et al. One needs to be cautious of results drawn from SLES.