The impact of incomplete lineage sorting (ILS) on phylogenetic conflicts among genes, and the related issue of whether to account for ILS in species tree reconstruction, are matters of intense controversy. Here, focusing on full-genome data in placental mammals, we empirically test two assumptions underlying current usage of tree-building methods that account for ILS. We show that in this dataset (i) distinct exons from a common gene do not share a common genealogy, and (ii) ILS is only a minor determinant of the existing phylogenetic conflict. These results shed new light on the relevance and conditions of applicability of ILS-aware methods in phylogenomic analyses of protein coding sequences.