BAMM (Bayesian Analysis of Macroevolutionary Mixtures) is a statistical framework that uses reversible jump MCMC to infer complex macroevolutionary dynamics of diversification and phenotypic evolution on phylogenetic trees. A recent article by Moore and coauthors (MEA) reported a number of theoretical and practical concerns with BAMM. Major claims from MEA are that (1) BAMM's likelihood function is incorrect, because it does not account for unobserved rate shifts; (2) the posterior distribution on the number of rate shifts is overly sensitive to the prior; and (3) diversification rate estimates from BAMM are unreliable. Here, we show that these and other conclusions from MEA are generally incorrect or unjustified. We first demonstrate that MEA's numerical assessment of the BAMM likelihood is compromised by their use of an invalid likelihood function. We then show that “unobserved rate shifts” appear to be irrelevant for biologically-plausible parameterizations of the diversification process. We find that the purportedly extreme prior sensitivity reported by MEA cannot be replicated with standard usage of BAMM v2.5, or with any other version, when conventional Bayesian model selection is performed. Finally, we demonstrate that BAMM performs very well at estimating diversification rate variation across the ∼20% of simulated trees in MEA's dataset for which it is theoretically possible to infer rate shifts with confidence. Due to ascertainment bias, the remaining 80% of their purportedly variable-rate phylogenies are statistically indistinguishable from those produced by a constant-rate birth-death process and were thus poorly-suited for the summary statistics used in their performance assessment. We demonstrate that inferences about diversification rates have been accurate and consistent across all major previous releases of the BAMM software. We recognize an acute need to address the theoretical foundations of rate-shift models for phylogenetic trees, and we expect BAMM and other modeling frameworks to improve in response to mathematical and computational innovations. However, we remain optimistic that that the imperfect tools currently available to comparative biologists have provided and will continue to provide important insights into the diversification of life on Earth.