Large-scale dynamics of the brain are routinely modelled us- ing systems of nonlinear dynamical equations that describe the evolution of population-level activity, with distinct neural pop- ulations often coupled according to an empirically measured structural connection matrix. This modelling approach has been used to generate insights into the neural underpinnings of spontaneous brain dynamics, as recorded with techniques such as resting state functional MRI (fMRI). In fMRI, researchers have many degrees of freedom in the way that they can pro- cess the data and recent evidence indicates that the choice of pre-processing steps can have a major effect on empirical esti- mates of functional connectivity. However, the potential influ- ence of such variations on modelling results are seldom consid- ered. Here we show, using three popular whole-brain dynam- ical models, that different choices during fMRI preprocessing can dramatically affect model fits and interpretations of find- ings. Critically, we show that the ability of these models to ac- curately capture patterns in fMRI dynamics is mostly driven by the degree to which they fit global signals rather than inter- esting sources of coordinated neural dynamics. We show that widespread deflections can arise from simple global synchroni- sation. We introduce a simple two-parameter model that cap- tures these fluctuations and which performs just as well as more complex, multi-parameter biophysical models. From our com- bined analyses of data and simulations, we describe benchmarks to evaluate model fit and validity. Although most models are not resilient to denoising, we show that relaxing the approxima- tion of homogeneous neural populations by more explicitly modelling inter-regional effective connectivity can improve model accuracy at the expense of increased model complexity. Our results suggest that many complex biophysical models may be fitting relatively trivial properties of the data, and underscore a need for tighter integration between data quality assurance and model development.