Support for Amborella as the sole survivor of an evolutionary lineage that is sister to all other angiosperms comes from positions in DNA multiple-sequence alignments that have a poor fit to time-reversible substitution models. These sites exhibit significant levels of homoplasy, compositional heterogeneity, and strong heterotachy. We report phylogenetic analyses with observed, randomized, and simulated data which show there is little or no expectation that these sites provide useful information for understanding relationships among basal angiosperms. Their inclusion in phylogenetic analyses leads to a long-branch attraction artifact that favors Amborella as sister to other angiosperms in reconstructed phylogenies. Using parametric simulations, we show that sites in chloroplast sequences that exhibit less homoplasy between angiosperms and gymnosperms provide more reliable information for inferring basal angiosperm relationships. We confirm our earlier findings that the basal angiosperm Amborella is most closely related to aquatic herbs. Our current and previously reported (Goremykin et al. 2013) analyses highlight an essential aspect of the total evidence approach to phylogenetic inference. They suggest that data partitioning aimed at identifying components of the data that better fit evolutionary models is a more reliable approach to phylogeny reconstruction at deep taxonomic levels.