In times of uncertainty, people often seek out information to help alleviate fear, possibly leaving them vulnerable to false information. During the COVID-19 pandemic, we attended to a viral spread of incorrect and misleading information that compromised collective actions and public health measures to contain the spread of the disease. We investigated the influence of fear of COVID-19 on social and cognitive factors including believing in fake news, bullshit receptivity, overclaiming, and problem-solving—within two of the populations that have been severely hit by COVID-19: Italy and the United States of America. To gain a better understanding of the role of misinformation during the early height of the COVID-19 pandemic, we also investigated whether problem-solving ability and socio-cognitive polarization were associated with believing in fake news. Results showed that fear of COVID-19 is related to seeking out information about the virus and avoiding infection in the Italian and American samples, as well as a willingness to share real news (COVID and non-COVID-related) headlines in the American sample. However, fear positively correlated with bullshit receptivity, suggesting that the pandemic might have contributed to creating a situation where people were pushed toward pseudo-profound existential beliefs. Furthermore, problem-solving ability was associated with correctly discerning real or fake news, whereas socio-cognitive polarization was the strongest predictor of believing in fake news in both samples. From these results, we concluded that a construct reflecting cognitive rigidity, neglecting alternative information, and black-and-white thinking negatively predicts the ability to discern fake from real news. Such a construct extends also to reasoning processes based on thinking outside the box and considering alternative information such as problem-solving.