The proliferation of misinformation on social media has become a significant concern, particularly in the realms of political discourse and public health. Censorship policies have emerged as a solution to limit the spread of misinformation. However, although censorship reduces the proportion of misinformation disseminated, it also creates an implied truth effect which skews the perception of less reliable information. This paper investigates the impact of censorship policies in an online social network model where agents sequentially observe an article and decide whether to share it with others or not. We measure the impact of censorship in the virality of articles containing misinformation and observe that while censorship can effectively reduce the spread of misinformation, it also allows less reliable articles to spread over the network. Specifically, we quantify the ``price of censorship'', a variation of the price of anarchy, associated with these censorship policies using a formal model that incorporates agents' beliefs, network structure, and content reliability. Unlike usual frameworks of resources allocation games in commutation networks, we show that the price of censorship is unbounded and we exhibit minimal limit case scenarios.