Embedded hierarchical structures, such as "the rat the cat ate was brown", constitute a core generative property of a natural language theory. Several recent studies have reported learning of hierarchical embeddings in artificial grammar learning (AGL) tasks, and described the functional specificity of Broca's area for processing such structures. In two experiments, we investigated whether alternative strategies can explain the learning success in these studies. We trained participants on hierarchical sequences, and found no evidence for the learning of hierarchical embeddings in test situations identical to those from other studies in the literature. Instead, participants appeared to solve the task by exploiting surface distinctions between legal and illegal sequences, and applying strategies such as counting or repetition detection. We suggest alternative interpretations for the observed activation of Broca's area, in terms of the application of calculation rules or of a differential role of working memory. We claim that the learnability of hierarchical embeddings in AGL tasks remains to be demonstrated.