Genome phylogenies are used to build tree-like representations of evolutionary relationships among genomes. However, in condensing the phylogenetic signals within a set of genomes down to a single tree, these methods generally do not explicitly take into account discordant signals arising due to lateral genetic transfer. Because conflicting vertical and horizontal signals can produce compromise trees that do not reflect either type of history, it is essential to understand the sensitivity of inferred genome phylogenies to these confounding effects. Using replicated simulations of genome evolution, we show that different scenarios of lateral genetic transfer have significant impacts on the ability to recover the "true" tree of genomes, even when corrections for phylogenetically discordant signals are used.