Adaptability is at the center of many important organizational challenges. In this work, we study the connection between network structure and collective adaptability to a shifting environment. Prior research has shown that network centralization — the degree to which communication flows disproportionately through one or more members of the organization rather than being more equally distributed — interferes with collective problem-solving by interfering with effective integration of existing ideas, information, and solutions in the network. We hypothesize that the mechanisms that are responsible for that poor integration of ideas, information, and solutions would prove beneficial for problems requiring adaptation to a shifting environment. We conducted a 1,620-subject randomized online laboratory experiment, testing the effect of seven network structures on problem-solving success. To simulate a shifting environment, we designed a murder mystery task and manipulated when each piece of information could be found: early information encouraged an incorrect consensus, requiring a collective shift of solution when more information emerged later. We find that when the communication network within an organization is more centralized, it achieves the benefits of social influence (learning) without the costs (herding). We also find, however, that these benefits of centralization come with a major caveat: they only materialize in networks with two-way flow of information and not when information only flows from the center of the network outwards (as can occur in hierarchical structures or digitally mediated communication). We draw on these findings to re-conceptualize theory on the impact of centralization on collective intelligence in problem-solving that demands collective adaptation by an organization’s members.