In a recent paper by Valensise et al [1], the authors present an analysis of social media data – from Facebook and Twitter – and vaccine hesitancy data – from Facebook – to provide evidence that the overabundance of potentially unreliable information, known as infodemic, does not affect vaccine acceptance. If confirmed, this result could have a dramatic impact on public health policies across the world, suggesting that current actions taken in place to contain and prevent the spreading of disinformation and misinformation might be useless to significantly hinder vaccine hesitancy. We disagree with this conclusion on the basis of existing literature that the authors fail to consider,of methodological concerns that suggest that their approach might have crucial flaws, and of an alternative empirical analysis unraveling a broader and richer picture to interpret.Simplistic analyses are not enough to assess the complex interplay between two complex social and behavioral phenomena such as vaccine hesitancy and infodemic: more sophisticated analyses are needed to account for the different intervening socio-cultural, behavioral, environmental and epidemiological factors. Under these conditions, we conclude that the authors’ main claim is conceptually and empirically unsupported. We are sincerely concerned that, if measures disregarding the circulating disinformation around the COVID19 vaccines were endorsed by policy makers in the design of future public health policies, it might lead to serious negative consequences by dangerously overlooking a major potential driver of dysfunctional behavioral responses to public health policies and goals.