Ferrigno et al. [2020] introduced an ingenious task to investigate recursion in human and non-human primates. American adults, Tsimane adults, and 3-5 year-old children successfully performed the task. Macaque monkeys required additional training, but two out of three eventually showed good generalization and scored above many Tsimane and child participants. Moreover, when tested on sequences composed of new bracket signs, the monkeys still showed good performance. The authors thus concluded that recursive nesting is not unique to humans. Here, we dispute the claim by showing that at least two alternative interpretations remain tenable. We first examine this conclusion in light of recent findings from modern artificial recurrent neural networks (RNNs), regarding how these networks encode sequences. We show that although RNNs, like monkeys, succeed on demanding generalization tasks as in Ferrigno et al., the underlying neural mechanisms are not recursive. Moreover, we show that when the networks are tested on sequences with deeper center-embedded structures compared to training, the networks fail to generalize. We then discuss an additional interpretation of the results in light of a simple model of sequence memory.