Squamate reptiles are a major component of vertebrate biodiversity whose crown-clade traces its origin to a narrow window of time in the Mesozoic during which the main subclades diverged in rapid succession. Deciphering phylogenetic relationships among these lineages has proven challenging given the conflicting signals provided by genomic and phenomic data. Most notably, the placement of Iguania has routinely differed between data sources, with morphological evidence supporting a sister relationship to the remaining squamates (Scleroglossa hypothesis) and molecular data favoring a highly nested position alongside snakes and anguimorphs (Toxicofera hypothesis). We provide novel insights by generating an expanded morphological dataset and exploring the presence of phylogenetic signal, noise, and biases in molecular data. Our analyses confirm the presence of strong conflicting signals for the position of Iguania between morphological and molecular datasets. However, we also find that molecular data behave highly erratically when inferring the deepest branches of the squamate tree, a consequence of limited phylogenetic signal to resolve this ancient radiation with confidence. This, in turn, seems to result from a rate of evolution that is too high for historical signals to survive to the present. Finally, we detect significant systematic biases, with iguanians and snakes sharing faster rates of molecular evolution and a similarly biased nucleotide composition. A combination of scant phylogenetic signal, high levels of noise, and the presence of systematic biases could result in the misplacement of Iguania. We regard this explanation to be at least as plausible as the complex scenario of convergence and reversals required for morphological data to be misleading. We further evaluate and discuss the utility of morphological data to resolve ancient radiations, as well as its impact in combined-evidence phylogenomic analyses, with results relevant for the assessment of evidence and conflict across the Tree of Life.