Mutualistic interactions, those that are naturally beneficial for both interacting species, are recurrently found in ecosystems. Observations of natural systems show that if we draw mutualistic relationships as links between species, the resulting mutualistic network of interactions displays a widespread particular ordering called nestedness. In such an ordering, the mutualistic partners of a given species conform a subset of the partners of all species with larger degree, that is, of those species having more interactions. On the other hand, theoretical works show that a nested structure has a positive impact on a number of relevant features of mutualistic communities ranging from species coexistence to structural stability and biodiversity. However, how nestedness emerges and what are its determinants, are still open challenges that have led to multiple debates to date. Here we show, by applying a theoretical approach to the analysis of 167 real mutualistic networks, that nestedness is not an irreducibly macroscopic feature but an entropic consequence of the degree sequences (number of mutualistic interactions of each species). Remarkably, we find that an outstanding majority of the analyzed networks does not show statistically significant nestedness. These findings point to the need of revising previous claims about the role of nestedness and might contribute to expand our understanding of how evolution shapes mutualistic interactions and communities by placing the focus on the node-dependent properties rather than on global quantities.