Sentences contain structure that determines their meaning beyond that of individual words. An influential study by Ding and colleagues (2016) used frequency tagging of phrases and sentences to show that the human brain is sensitive to structure by finding peaks of neural power at the rate at which structures were presented. Since then, there has been a rich debate on how to best explain this pattern of results with profound impact on the language sciences. Models that use hierarchical structure building, as well as models based on associative sequence processing, can predict the neural response, creating an inferential impasse as to which class of models explains the nature of the linguistic computations reflected in the neural readout. In the current manuscript, we discuss pitfalls and common fallacies seen in the conclusions drawn in the literature illustrated by various simulations. We conclude that inferring the neural operations of sentence processing based on these neural data, and any like it, alone, is insufficient. We discuss how to best evaluate models and how to approach the modeling of neural readouts to sentence processing in a manner that remains faithful to cognitive, neural, and linguistic principles.