Adams and Collyer argue that contemporary multivariate (Gaussian) phylogenetic comparative methods are prone to favouring more complex models of evolution and sometimes rotation invariance can be an issue. Here we dissect the concept of rotation invariance and point out that, depending on the understanding, this can be an issue with any method that relies on numerical instead of analytical estimation approaches. We relate this to the ongoing discussion concerning phylogenetic principal component analysis. Contrary to what Adams and Collyer found, we do not observe a bias against the simpler Brownian motion process in simulations when we use the new, improved, likelihood evaluation algorithm employed by mvSLOUCH, which allows for studying much larger phylogenies and more complex model setups.