Recent models of movement generation in motor cortex have sought to explain neural activity not as a function of movement parameters, known as representational models, but as a dynamical system acting at the level of the population. Despite evidence supporting this framework, the evaluation of representational models and their integration with dynamical systems is incomplete in the literature. Using a representational velocity-tuning based simulation of center-out reaching, we show that incorporating variable latency offsets between neural activity and kinematics is sufficient to generate rotational dynamics at the level of neural populations, a phenomenon observed in motor cortex. However, we developed a covariance-matched permutation test (CMPT) that reassigns neural data between task conditions independently for each neuron while maintaining overall neuron-to-neuron relationships, revealing that rotations based on the representational model did not uniquely depend on the underlying condition structure. In contrast, rotations based on either a dynamical model or motor cortex data depend on this relationship, providing evidence that the dynamical model more readily explains motor cortex activity. Importantly, implementing a recurrent neural network we demonstrate that both representational tuning properties and rotational dynamics emerge, providing evidence that a dynamical system can reproduce previous findings of representational tuning. Finally, using motor cortex data in combination with the CMPT, we show that results based on small numbers of neurons or conditions should be interpreted cautiously, potentially informing future experimental design. Together, our findings reinforce the view that representational models lack the explanatory power to describe complex aspects of single neuron and population level activity.